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2-positive contractive projections on noncommutative Lp-spaces J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-26 Cédric Arhancet, Yves Raynaud
We prove the first theorem on projections on general noncommutative -spaces associated with non-type I von Neumann algebras where . This is the first progress on this topic since the seminal work of Arazy and Friedman (1992) where the problem of the description of contractively complemented subspaces of noncommutative -spaces is explicitly raised. We show that the range of a 2-positive contractive
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Global existence for an isotropic modification of the Boltzmann equation J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-26 Stanley Snelson
Motivated by the open problem of large-data global existence for the non-cutoff Boltzmann equation, we introduce a model equation that in some sense disregards the anisotropy of the Boltzmann collision kernel. We refer to this model equation as by analogy with the isotropic Landau equation introduced by Krieger and Strain (2012) . The collision operator of our isotropic Boltzmann model converges to
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Unconditional bases and Daugavet renormings J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-26 Rainis Haller, Johann Langemets, Yoël Perreau, Triinu Veeorg
We prove that the space – and more generally every infinite dimensional Banach space with an unconditional Schauder basis – can be renormed to have a Daugavet point. As a starting point, we introduce a new diametral notion for points of the unit sphere of Banach spaces, that complements the notion of Δ-points, but is weaker than the notion of Daugavet points. We show that this notion can be used to
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A short proof of Tomita's theorem J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-26 Jonathan Sorce
Tomita-Takesaki theory associates a positive operator called the “modular operator” with a von Neumann algebra and a cyclic-separating vector. Tomita's theorem says that the unitary flow generated by the modular operator leaves the algebra invariant. I give a new, short proof of this theorem which only uses the analytic structure of unitary flows, and which avoids operator-valued Fourier transforms
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Nonlinear random perturbations of PDEs and quasi-linear equations in Hilbert spaces depending on a small parameter J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-26 Sandra Cerrai, Giuseppina Guatteri, Gianmario Tessitore
We study a class of quasi-linear parabolic equations defined on a separable Hilbert space, depending on a small parameter in front of the second order term. Through the nonlinear semigroup associated with such equation, we introduce the corresponding SPDE and we study the asymptotic behavior of its solutions, depending on the small parameter. We show that a large deviations principle holds and we give
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Ginzburg-Landau equation and Meissner states of multiply-connected superconductors J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-26 Xing-Bin Pan
This paper concerns the Ginzburg-Landau equation and the Meissner equations on a bounded multiply-connected domain in . The novelty of these equations is that both of them contain an unknown potential and an unknown Neumann field as the Lagrange multipliers. The minimal and non-minimal solutions for each equation are obtained by variational methods, and the effect of the applied magnetic field on the
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Harmonic oscillator on Weyl chambers J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-26 Krzysztof Stempak
Let denote a Weyl chamber distinguished in the framework of a finite reflection group acting on . We consider the harmonic oscillator as an operator on with appropriately chosen domains and construct families of corresponding self-adjoint extensions. These extensions are parametrized by the homomorphisms and are based on an -symmetrization procedure of functions on the whole . The analysis of the associated
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Small spheres with prescribed nonconstant mean curvature in Riemannian manifolds J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-26 Alberto Enciso, Antonio J. Fernández, Daniel Peralta-Salas
Given a function on a smooth Riemannian manifold without boundary, we prove that if is a non-degenerate critical point of , then a neighborhood of contains a foliation by spheres with mean curvature proportional to . This foliation is essentially unique. The nondegeneracy assumption can be substantially relaxed, at the expense of losing the property that the family of spheres with prescribed mean curvature
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Rational approximation of operator semigroups via the [formula omitted]-calculus J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-25 Alexander Gomilko, Yuri Tomilov
We improve the classical results by Brenner and Thomée on rational approximations of operator semigroups. In the setting of Hilbert spaces, we introduce a finer regularity scale for initial data, provide sharper stability estimates, and obtain optimal approximation rates. Moreover, we strengthen a result due to Egert-Rozendaal on subdiagonal Padé approximations of operator semigroups. Our approach
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The Pólya-Szegő inequality for smoothing rearrangements J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-25 Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi, Markus Kiderlen
A basic version of the Pólya-Szegő inequality states that if Φ is a Young function, the Φ-Dirichlet energy—the integral of —of a suitable function , the class of nonnegative measurable functions on that vanish at infinity, does not increase under symmetric decreasing rearrangement. This fact, along with variants that apply to polarizations and to Steiner and certain other rearrangements, has numerous
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Orthonormal Strichartz estimate for dispersive equations with potentials J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-25 Akitoshi Hoshiya
In this paper we prove the orthonormal Strichartz estimates for the higher order and fractional Schrödinger, wave, Klein-Gordon and Dirac equations with potentials. As in the case of the Schrödinger operator, the proofs are based on the smooth perturbation theory by T. Kato. However, for the Klein-Gordon and Dirac equations, we also use a method of the microlocal analysis in order to prove the estimates
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Regular ellipsoids and a Blaschke-Santaló-type inequality for projections of non-symmetric convex bodies J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-20 Beatrice-Helen Vritsiou
It is shown that every not-necessarily symmetric convex body in has an affine image of such that the covering numbers of by growing dilates of the unit Euclidean ball, as well as those of the unit Euclidean ball by growing dilates of , decrease in a regular way. This extends to the non-symmetric case a famous theorem by Pisier, albeit with worse estimates on the rate of decrease of the covering numbers
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The automatic imprimitivity for Gq J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-20 Mao Hoshino
Let be the Drinfeld-Jimbo deformation of a connected simply-connected compact Lie group and be its maximal torus. We show that the induction functors from the categories of -equivariant correspondences to the categories of -equivariant correspondences give equivalences of these categories under the existence of tracial states. As its application, we show some automatic imprimitivity results and classification
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Phase retrieval of entire functions and its implications for Gabor phase retrieval J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 Matthias Wellershoff
We characterise all pairs of finite order entire functions whose magnitudes agree on two arbitrary lines in the complex plane by means of the Hadamard factorisation theorem. Building on this, we also characterise all pairs of second order entire functions whose magnitudes agree on infinitely many equidistant parallel lines. Furthermore, we show that the magnitude of an entire function on three parallel
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On rationality of spectrums for spectral sets in [formula omitted] J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 Weiqi Zhou
Let be a compact measurable set of measure 1 and with null boundary measure. We show that if Ω is a spectral set, then it admits a rational spectrum. The proof relies on the periodicity of spectrums shown in , and adopts the technique in for analyzing zeros of exponential sums as well as the technique in that relates the spectrum to the tiling of . The key technical ingredient we contribute that eventually
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Quantitative asymptotic stability of the quasi-linearly stratified densities in the IPM equation with the sharp decay rates J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 Min Jun Jo, Junha Kim
We analyze the asymptotic stability of the quasi-linearly stratified densities in the 2D inviscid incompressible porous medium equation on with respect to the buoyancy frequency . Our target density of stratification is the sum of the large background linear profile with its slope and the small perturbation that could be both non-linear and non-monotone. Quantification in will be performed not only
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On quantum Sobolev inequalities J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 Laurent Lafleche
We investigate the quantum analogue of the classical Sobolev inequalities in the phase space, with the quantum Sobolev norms defined in terms of Schatten norms of commutators. These inequalities provide an uncertainty principle for the Wigner–Yanase skew information, and also lead to new bounds on the Schatten norms of the Weyl quantization in terms of its symbol. As an intermediate tool, we obtain
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Generalized Schrödinger operators on the Heisenberg group and Hardy spaces J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 The Anh Bui, Qing Hong, Guorong Hu
Let be a generalized Schrödinger operator on the Heisenberg group , where is the sub-Laplacian, and is a nonnegative Radon measure satisfying certain conditions. In this paper, we first establish some estimates of the fundamental solution and the heat kernel of . Applying these estimates, we then study the Hardy spaces introduced in terms of the maximal function associated with the heat semigroup ;
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Negative powers of Hilbert-space contractions J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 Thomas Ransford
We show that, given a closed subset of the unit circle of Lebesgue measure zero, there exists a positive sequence with the following property: if is a Hilbert-space contraction such that and and , then is a unitary operator. We further show that the condition of measure zero is sharp.
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Capacitary maximal inequalities and applications J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 You-Wei Benson Chen, Keng Hao Ooi, Daniel Spector
In this paper we introduce capacitary analogues of the Hardy-Littlewood maximal function, for = the Hausdorff content or a Riesz capacity. For these maximal functions, we prove a strong-type bound for on the capacitary integration spaces and a weak-type bound on the capacitary integration space . We show how these estimates clarify and improve the existing literature concerning maximal function estimates
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The reciprocal Kirchberg algebras J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 Taro Sogabe
For two unital Kirchberg algebras with finitely generated K-groups, we introduce a property, called reciprocality, which is proved to be closely related to the homotopy theory of Kirchberg algebras. We show the Spanier–Whitehead duality for bundles of separable nuclear UCT C*-algebras with finitely generated K-groups and conclude that two reciprocal Kirchberg algebras share the same structure of their
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A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-13 Jiayin Liu, Shijin Zhang, Yuan Zhou
We build up a quantitative second-order Sobolev estimate of for positive -harmonic functions in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted -harmonic functions in weighted manifolds under the Bakry-Émery curvature-dimension condition.
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Finite speed axially symmetric Navier-Stokes flows passing a cone J. Funct. Anal. (IF 1.7) Pub Date : 2024-03-06 Zijin Li, Xinghong Pan, Xin Yang, Chulan Zeng, Qi S. Zhang, Na Zhao
Let be the exterior of a cone inside a ball, with its altitude angle at most in , which touches the axis at the origin. For any initial value in a class, which has the usual even-odd-odd symmetry in the variable and has the partial smallness only in the swirl direction: , the axially symmetric Navier-Stokes equations (ASNS) with Navier-Hodge-Lions slip boundary condition have a finite-energy solution
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A uniform trace theorem for Dirichlet forms on Sierpinski fractals J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Jiejie Cai, Hua Qiu, Yizhou Wang
We establish trace theorems for the self-similar Dirichlet forms on the Sierpinski gasket and the Sierpinski carpet to their subsets generated by cutting with a straight line. For the Sierpinski gasket, the straight line can be in any direction. For the Sierpinski carpet, we require the straight line parallel to an edge of the carpet. The trace forms are expressed in term of values of functions along
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Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Tullio Ceccherini-Silberstein, Michel Coornaert, Hanfeng Li
A dynamical system is a pair , where is a compact metrizable space and is a countable group acting by homeomorphisms of . An endomorphism of is a continuous selfmap of which commutes with the action of . One says that a dynamical system is surjunctive provided that every injective endomorphism of is surjective (and therefore is a homeomorphism). We show that when is sofic, every expansive dynamical
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The H2-Corona problem on delta-regular domains J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Bo-Yong Chen, Xu Xing
We prove an -Corona theorem with estimate for on delta-regular domains, where and is the number of generators. This class of domains includes smooth bounded domains with defining functions that are plurisubharmonic on boundaries and pseudoconvex domains of D'Angelo finite type.
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On topologically zero-dimensional morphisms J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Jorge Castillejos, Robert Neagu
We investigate -homomorphisms with nuclear dimension equal to zero. In the framework of classification of -homo-morphisms, we characterise such maps as those that can be approximately factorised through an AF-algebra.
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Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Gael Y. Diebou
We analyze the forced incompressible stationary Navier-Stokes flow in , . Existence of a unique solution satisfying a global integrability property measured in a scale of tent spaces is established for small data in homogeneous Sobolev space with degree of smoothness. The velocity field is shown to be locally Hölder continuous while the pressure belongs to for any . Our approach is based on the analysis
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Reiterated homogenization of parabolic systems with several spatial and temporal scales J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Weisheng Niu
We consider quantitative estimates in the homogenization of second-order parabolic systems with periodic coefficients that oscillate on multiple spatial and temporal scales, where , with and . The convergence rate in the homogenization is derived in the space, and the large-scale interior and boundary Lipschitz estimates are also established. In the case , such issues have been addressed by Geng and
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Alexandrov groupoids and the nuclear dimension of twisted groupoid C⁎-algebras J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Kristin Courtney, Anna Duwenig, Magdalena C. Georgescu, Astrid an Huef, Maria Grazia Viola
We consider a twist over an étale groupoid . When is principal, we prove that the nuclear dimension of the reduced twisted groupoid -algebra is bounded by a number depending on the dynamic asymptotic dimension of and the topological covering dimension of its unit space. This generalizes an analogous theorem by Guentner, Willett, and Yu for the -algebra of . Our proof uses a reduction to the unital
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On fully nonlinear Loewner-Nirenberg problem of Ricci curvature J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Zhenan Sui
We prove the existence of a smooth complete conformal metric with prescribed kth elementary symmetric function of negative Ricci curvature under certain condition on general domain in Euclidean space. We then formulate this problem for more general equations.
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Kähler–Einstein metrics and obstruction flatness II: Unit Sphere bundles J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Peter Ebenfelt, Ming Xiao, Hang Xu
This paper concerns obstruction flatness of hypersurfaces Σ that arise as unit sphere bundles of Griffiths negative Hermitian vector bundles over Kähler manifolds . We prove that if the curvature of satisfies a splitting condition and has constant Ricci eigenvalues, then is obstruction flat. If, in addition, all these eigenvalues are strictly less than one and is complete, then we show that the corresponding
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Nondivergence form degenerate linear parabolic equations on the upper half space J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Hongjie Dong, Tuoc Phan, Hung Vinh Tran
We study a class of nondivergence form second-order degenerate linear parabolic equations in with the homogeneous Dirichlet boundary condition on , where and is given. The coefficient matrices of the equations are the product of and bounded positive definite matrices, where behaves like for some given , which are degenerate on the boundary of the domain. Under a partially weighted VMO (vanishing mean
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Polyharmonic potential theory on the Poincaré disk J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Massimo A. Picardello, Maura Salvatori, Wolfgang Woess
We consider the open unit disk equipped with the hyperbolic metric and the associated hyperbolic Laplacian . For and , a -polyharmonic function of order is a function such that . If , one gets -harmonic functions. Based on a Theorem of Helgason on the latter functions, we prove a boundary integral representation theorem for -polyharmonic functions. For this purpose, we first determine -order -Poisson
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Sobolev homeomorphic extensions from two to three dimensions J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Stanislav Hencl, Aleksis Koski, Jani Onninen
We study the basic question of characterizing which boundary homeomorphisms of the unit sphere can be extended to a Sobolev homeomorphism of the interior in 3D space. While the planar variants of this problem are well-understood, completely new and direct ways of constructing an extension are required in 3D. We prove, among other things, that a Sobolev homeomorphism in for some admits a homeomorphic
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Fourier decay of fractal measures on surfaces of co-dimension two in R5 J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Zhenbin Cao, Changxing Miao, Zijian Wang
In this paper, we study the Fourier decay of fractal measures on the quadratic surfaces of high co-dimensions. Unlike the case of co-dimension 1, quadratic surfaces of high co-dimensions possess some special scaling structures and degenerate characteristics. We will adopt the strategy from Du and Zhang , combined with the broad-narrow analysis with different dimensions as divisions, to obtain a few
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On Fourier expansions for systems of ordinary differential equations with distributional coefficients J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Steven Redolfi, Rudi Weikard
We study the spectral theory for the first-order system of differential equations on the real interval where is a constant, invertible, skew-hermitian matrix and and are matrices whose entries are distributions of order 0 with hermitian and non-negative. Specifically, we construct a generalized Weyl-Titchmarsh -function with corresponding spectral measure and a generalized Fourier transform after imposing
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Sharp fractional Hardy inequalities with a remainder for 1 < p < 2 J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Bartłomiej Dyda, Michał Kijaczko
The main purpose of this article is to obtain (weighted) fractional Hardy inequalities with a remainder and fractional Hardy–Sobolev–Maz'ya inequalities valid for .
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Dispersion for the wave equation outside a cylinder in [formula omitted] J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-15 Felice Iandoli, Oana Ivanovici
We consider the wave equation with Dirichlet boundary conditions in the exterior of a cylinder in and we construct a global in time parametrix to derive sharp dispersion estimates for all frequencies (low and high) and, as a corollary, Strichartz estimates, all matching the case.
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On (global) unique continuation properties of the fractional discrete Laplacian J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-14 Aingeru Fernández-Bertolin, Luz Roncal, Angkana Rüland
We study various qualitative and quantitative (global) unique continuation properties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (global) unique continuation properties, the fractional discrete Laplacian does not enjoy these in general. While discretization thus counteracts the strong rigidity properties of the
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Martingale type, the Gamlen-Gaudet construction and a greedy algorithm J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-13 Krystian Kazaniecki, Paul F.X. Müller
In the present paper we identify those filtered probability spaces that determine already the martingale type of a Banach space . We isolate intrinsic conditions on the filtration of purely atomic -algebras which determine that the upper estimates imply that the Banach space X is of martingale type . Our paper complements G. Pisier's investigation and continues the work by S. Geiss and second named
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Sobolev embeddings for kinetic Fokker-Planck equations J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-29 Andrea Pascucci, Antonello Pesce
We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak Hörmander condition. We prove continuous embeddings into Lorentz and intrinsic Hölder spaces. We also prove approximation and interpolation inequalities by means of an intrinsic Taylor expansion, extending analogous results for Hölder spaces. The embedding at first order is
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On unitary groups of crossed product von Neumann algebras J. Funct. Anal. (IF 1.7) Pub Date : 2024-02-01 Yasuhito Hashiba
We consider the tracial crossed product algebra arising from a trace preserving action of a discrete group Λ on a tracial von Neumann algebra . For a unitary subgroup , we study when this can be conjugated into in . We provide a general sufficient condition for this to happen. Our result generalizes which treats the case when is the group von Neumann algebra .
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Geometry of unit balls of free Banach lattices, and its applications J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-29 T. Oikhberg
We begin by describing the unit ball of the free p-convex Banach lattice over a Banach space E (denoted by FBL(p)[E]) as a closed solid convex hull of an appropriate set. Based on it, we show that, if a Banach space E has the λ-Approximation Property, then FBL(p)[E] has the λ-Positive Approximation Property. Further, we show that operators u∈B(E,F) (where E and F are Banach spaces) which extend to
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On the local uniqueness of steady states for the Vlasov-Poisson system J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-29 Mikaela Iacobelli
Motivated by the results of Lemou, Méhats, and Räphael [16] and Lemou [15] concerning the quantitative stability of some suitable steady states for the Vlasov-Poisson system, we investigate the local uniqueness of steady states near these ones. This is inspired by analogous results of Choffrut and Šverák in the context of the 2D Euler equations [6].
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On bodies in Rn with congruent sections by cones or non-central planes J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-29 Junling Li, Ning Zhang
Let K and L be two convex bodies in Rn, n≥3 such that their sections by cones {x∈Rn:x⋅ξ=t|x|} or non-central planes with a fixed distance from the origin are directly congruent. We prove that if their boundaries are of class C2, then K and L coincide.
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Traces on ultrapowers of C*-algebras J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-27 Ramon Antoine, Francesc Perera, Leonel Robert, Hannes Thiel
Using Cuntz semigroup techniques, we characterize when limit traces are dense in the space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density of limit quasitraces on ultraproducts of C*-algebras. Quite unexpectedly, we obtain as an application that every simple C*-algebra that is (m,n)-pure in the sense of Winter is already pure. As another application, we provide
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Multiplicity of solutions to the multiphasic Allen–Cahn–Hilliard system with a small volume constraint on closed parallelizable manifolds J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-27 João Henrique Andrade, Jackeline Conrado, Stefano Nardulli, Paolo Piccione, Reinaldo Resende
We prove the existence of multiple solutions to the Allen–Cahn–Hilliard (ACH) vectorial equation (with two equations) involving a triple-well (triphasic) potential with a small volume constraint on a closed parallelizable Riemannian manifold. More precisely, we find a lower bound for the number of solutions depending on some topological invariants of the underlying manifold. The phase transition potential
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Generalized common index jump theorem with applications to closed characteristics on star-shaped hypersurfaces and beyond J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-27 Huagui Duan, Hui Liu, Yiming Long, Wei Wang
In this paper, we first generalize the common index jump theorem of Long-Zhu in 2002 and Duan-Long-Wang in 2016 to the case where the mean indices of symplectic paths are not required to be all positive. As applications, we study closed characteristics on compact star-shaped hypersurfaces in R2n, when both positive and negative mean indices may appear simultaneously. Specially we establish the existence
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Group extensions preserve almost finiteness J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-26 Petr Naryshkin
We show that a free action G↷X is almost finite if its restriction to some infinite normal subgroup of G is almost finite. Consider the class of groups which contains all infinite groups of locally subexponential growth and is closed under taking direct limits and extensions on the right by any amenable group. It follows that all free actions of a group from this class on finite-dimensional spaces
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Weighted Sobolev spaces and Morse estimates for quasilinear elliptic equations J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-26 Silvia Cingolani, Marco Degiovanni, Berardino Sciunzi
We establish critical groups estimates for the weak solutions of −Δpu=f(x,u) in Ω and u=0 on ∂Ω via Morse index, where Ω is a bounded domain, f∈C1(Ω‾×R) and f(x,s)>0 for all x∈Ω‾, s>0 and f(x,s)=0 for all x∈Ω‾, s≤0. The proof relies on new uniform Sobolev inequalities for approximating problems. We also prove critical groups estimates when Ω is the ball or the annulus and f is a sign changing function
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Landscape approximation of the ground state eigenvalue for graphs and random hopping models J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-26 L. Shou, W. Wang, S. Zhang
We consider the localization landscape function u and ground state eigenvalue λ for operators on graphs. We first show that the maximum of the landscape function is comparable to the reciprocal of the ground state eigenvalue if the operator satisfies certain semigroup kernel upper bounds. This implies general upper and lower bounds on the landscape product λ‖u‖∞ for several models, including the Anderson
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The CCAP for graph products of operator algebras J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-26 Matthijs Borst
For a simple graph Γ and for unital C*-algebras with GNS-faithful states (Av,φv) for v∈VΓ, we consider the reduced graph product (A,φ)=⁎v,Γ(Av,φv), and show that if every C*-algebra Av has the completely contractive approximation property (CCAP) and satisfies some additional condition, then the graph product has the CCAP as well. The additional condition imposed is satisfied in natural cases, for example
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Reversible Coalescing-Fragmentating Wasserstein Dynamics on the Real Line J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-26 Vitalii Konarovskyi, Max-K. von Renesse
We introduce a family of reversible fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction on the real line as mathematically rigorous description of colloidal motion of fluids. The associated measure-valued process provides a weak solution to a corrected Dean–Kawasaki equation for supercooled liquids without dissipation. Our construction
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Trace distance ergodicity for quantum Markov semigroups J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-27 Lorenzo Bertini, Alberto De Sole, Gustavo Posta
We discuss the quantitative ergodicity of quantum Markov semigroups in terms of the trace distance from the stationary state, providing a general criterion based on the spectral decomposition of the Lindblad generator. We then apply this criterion to the bosonic and fermionic Ornstein-Uhlenbeck semigroups and to a family of quantum Markov semigroups parametrized by semisimple Lie algebras and their
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Intrinsic dimensional functional inequalities on model spaces J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-26 Alexandros Eskenazis, Yair Shenfeld
We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of constant curvature. In the latter settings, our intrinsic dimensional functional inequalities improve on a series of known results and lead to new Hamilton-type matrix
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Global martingale weak solutions for the three-dimensional stochastic chemotaxis-Navier-Stokes system with Lévy processes J. Funct. Anal. (IF 1.7) Pub Date : 2024-01-26 Lei Zhang, Bin Liu
This paper considers the three-dimensional stochastic chemotaxis-Navier-Stokes (SCNS) system subjected to a Lévy-type random external force in a bounded domain. Until recently, the existed results concerning global solvability of SCNS system mainly concentrated on the case of two spatial dimensions, little is known about the SCNS system in dimension three. We prove in the present work that the initial-boundary