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Schur inequality for Murray–von Neumann algebras and its applications Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-18 Shavkat Ayupov, Jinghao Huang, Karimbergen Kudaybergenov
In this paper, we present a version of the Schur inequality in the setting of Murray–von Neumann algebras, extending a result by Arveson and Kadison. We also describe the ring isomorphisms between \(*\)-subalgebras of two Murray–von Neumann algebras. A short proof of the commutator estimation theorem for Murray–von Neumann algebras is given as an easy application.
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Toeplitz operators with monomial symbols on the Dirichlet spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-17 Sumin Kim, Jongrak Lee
In this paper, we are concerned with the various properties of the Toeplitz operators acting on the Dirichlet spaces. First, we consider the matrix representation of Toeplitz operators with harmonic and monomial symbols. Second, we establish the expansivity and contractivity of the Toeplitz operators \(T_{\varphi }\) with monomial symbols \(\varphi \). Third, we give a necessary and sufficient conditions
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Dixmier-type traces on symmetric spaces associated with semifinite von Neumann algebras Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-16 Galina Levitina, Alexandr Usachev
We prove that a normalised linear functional on certain symmetric spaces associated with a semifinite von Neumann algebra, respects tail majorisation if and only if it is a Dixmier-type trace.
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Normalized solutions of linear and nonlinear coupled Choquard systems with potentials Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-15 Zhenyu Guo, Wenyan Jin
In this paper, we study Choquard systems with linear and nonlinear couplings with different potentials under the \(L^2\)-constraint. We use Ekland variational principle to prove this system has a normalized radially symmetric solution for \(L^2\)-subcritical case when the dimension is greater than or equal to 2 without potentials. In addition, a positive solution with prescribed \(L^2\)-constraint
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New properties and existence of exact phase-retrievable g-frames Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-15 Miao He, Jingsong Leng
Due to the frame elements of the g-frames being operators, it has many differences from traditional frames. Hence some new characterizations of exact phase-retrievable g-frames from the perspective of operator theory are mainly discussed in this paper. Firstly, we find that for an exact phase-retrievable g-frame, its canonical dual frame will maintain the exact phase-retrievability. Then the stability
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On the decomposability for sums of complex symmetric operators Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-10 Sungeun Jung
In this paper, we study decomposability for sums of complex symmetric operators. As applications, we consider decomposable operator matrices.
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Some converse problems on the g-Drazin invertibility in Banach algebras Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-09 Honglin Zou
The main purpose of this paper is to investigate the converse problems of some well-known results related to the generalized Drazin (g-Drazin for short) inverse in Banach algebras. Let \({\mathcal {A}}\) be a Banach algebra and \(a,b\in {\mathcal {A}}\). First, we give the relationship between the Drazin (g-Drazin, group) invertibility of a, b and that of the sum \(a+b\) under certain conditions. Then
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Geometric constant for quantifying the difference between angular and skew angular distances in Banach spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-05 Yuankang Fu, Yongjin Li
This article is devoted to introduce a new geometric constant called Dehghan–Rooin constant, which quantifies the difference between angular and skew angular distances in Banach spaces. We quantify the characterization of uniform non-squareness in terms of Dehghan–Rooin constant. The relationships between Dehghan–Rooin constant and uniform convexity, Dehghan-Rooin constant and uniform smoothness are
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An extension of the weighted geometric mean in unital JB-algebras Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-05 A. G. Ghazanfari, S. Malekinejad, M. Sababheh
Let \({\mathcal {A}}\) be a unital JB-algebra and \(A,B\in {\mathcal {A}}\). The weighted geometric mean \(A\sharp _r B\) for \(A,B\in {\mathcal {A}}\) has been recently defined for \(r\in [0,1].\) In this work, we extend the weighted geometric mean \(A\sharp _r B\), from \(r\in [0,1]\) to \(r\in (-1, 0)\cup (1, 2)\). We will notice that many results will be reversed when the domain of r change from
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Hölder continuity of the gradients for non-homogenous elliptic equations of p(x)-Laplacian type Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-05 Fengping Yao
The main goal of this paper is to discuss the local Hölder continuity of the gradients for weak solutions of the following non-homogenous elliptic p(x)-Laplacian equations of divergence form $$\begin{aligned} \text {div} \left( \left( A(x) \nabla u(x) \cdot \nabla u(x) \right) ^{\frac{p(x)-2}{2}} A(x) \nabla u(x) \right) = \text {div} \left( |\textbf{f}(x) |^{p(x)-2} \textbf{f}(x) \right) ~~ \text{
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Martingale Hardy–Orlicz-amalgam spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-04 Libo Li, Kaituo Liu, Yao Wang
In this article, the authors first introduce a class of Orlicz-amalgam spaces, which defined on a probabilistic setting. Based on these Orlicz-amalgam spaces, the authors introduce a new kind of Hardy type spaces, namely martingale Hardy–Orlicz-amalgam spaces, which generalize the martingale Hardy-amalgam spaces very recently studied by Bansah and Sehba. Their characterizations via the atomic decompositions
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Characterization of a-Birkhoff–James orthogonality in $$C^*$$ -algebras and its applications Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-03
Abstract Let \({\mathcal {A}}\) be a unital \(C^*\) -algebra with unit \(1_{{\mathcal {A}}}\) and let \(a\in {\mathcal {A}}\) be a positive and invertible element. Suppose that \({\mathcal {S}}({\mathcal {A}})\) is the set of all states on \(\mathcal {{\mathcal {A}}}\) and let $$\begin{aligned} {\mathcal {S}}_a ({\mathcal {A}})=\left\{ \dfrac{f}{f(a)} \, : \, f \in {\mathcal {S}}({\mathcal {A}}), \
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The eigenvalues, numerical ranges, and invariant subspaces of the Bergman Toeplitz operators over the bidisk Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-02 Yongning Li, Yin Zhao, Xuanhao Ding
In this paper, we consider several questions about the eigenvalues, the numerical ranges, and the invariant subspaces of the Toeplitz operator on the Bergman space over the bidisk and we obtain the corresponding results.
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Characterizations for boundedness of fractional maximal function commutators in variable Lebesgue spaces on stratified groups Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-04-01 Wenjiao Zhao, Jianglong Wu
In this paper, the main aim is to consider the mapping properties of the maximal or nonlinear commutator for the fractional maximal operator with the symbols belong to the Lipschitz spaces on variable Lebesgue spaces in the context of stratified Lie groups, with the help of which some new characterizations to the Lipschitz spaces and nonnegative Lipschitz functions are obtained in the stratified groups
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The essential spectrums of $$2\times 2$$ unbounded anti-triangular operator matrices Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-03-31 Xinran Liu, Deyu Wu
Let $$\begin{aligned} {\mathcal {T}}=\left( \begin{array}{cc} 0 &{}\quad B \\ C &{}\quad D \\ \end{array} \right) :D(C)\times D(B)\subset X\times X\rightarrow X\times X \end{aligned}$$ be a \(2\times 2\) unbounded anti-triangular operator matrix on complex Hilbert space \(X\times X\). Using the relative compact perturbation theory and the space decomposition method, the seven essential spectrum equalities
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Harmonic Bloch space on the real hyperbolic ball Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-03-27 A. Ersin Üreyen
We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from \(L^\infty ({\mathbb {B}})\) to \({\mathcal {B}}\), and from \(C_0({\mathbb {B}})\) to \({\mathcal {B}}_0\) are onto. We verify that the dual space of the hyperbolic harmonic Bergman space \({\mathcal {B}}^1_\alpha \) is \({\mathcal {B}}\) and its predual is \({\mathcal
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The local Borg–Marchenko uniqueness theorem for Dirac-type systems with locally smooth at the right endpoint rectangular potentials Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-03-26 Tiezheng Li, Guangsheng Wei
We consider self-adjoint Dirac-type systems with rectangular matrix potentials on the interval [0, b), where \(0
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Application of Banach limits to invariant measures of infinite-dimensional Hamiltonian flows Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-03-21 V. Zh. Sakbaev
Applying an invariant measure on phase space, we study the Koopman representation of a group of symplectomorphisms in an infinite-dimensional Hilbert space equipped with a translation-invariant symplectic form. The phase space is equipped with a finitely additive measure, invariant under the group of symplectomorphisms generated by Liouville-integrable Hamiltonian systems. We construct an invariant
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M-serially summing operators on Banach lattices Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-03-16 Fu Zhang, Hanhan Shen, Zili Chen
Let E, F be Banach lattices, where E has the disjoint Riesz decomposition property. For a lattice homomorphism \(T:E\rightarrow F\) and a bounded subset A of E, we establish a necessary and sufficient condition under which TA is b-order bounded. Based on this, we study the b-order boundedness of subsets of E and obtain several characterizations of AM-spaces. Furthermore, we introduce and investigate
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Disjoint subspace-hypercyclic operators on separable Banach spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-03-14 Renyu Chen, Xiang Chen, Zehua Zhou
In this paper, we initially introduce the concept of disjoint subspace-hypercyclic operators and illustrate that disjoint subspace-hypercyclic operators differ from disjoint hypercyclic operators. Furthermore, we obtain two different criteria for disjoint subspace-hypercyclic operators. Finally, we discover an equivalent condition regarding the bilateral forward weighted shift operators’ disjoint
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Block dual Toeplitz operators on the orthogonal complement of the Dirichlet space Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-03-11 Chunxu Xu, Jianxiang Dong, Tao Yu
We give some characterizations of block dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space. We characterized the compactness of the finite sum of block dual Toeplitz products. Commuting block dual Toeplitz operators and quasinormal block dual Toeplitz operators are also considered.
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Some new weighted weak-type iterated and bilinear modified Hardy inequalities Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-03-02
Abstract We characterize the good weights for some weighted weak-type iterated and bilinear modified Hardy inequalities to hold.
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Common properties of a and b satisfying $$ab^n = b^{n+1}$$ and $$ba^n = a^{n+1}$$ in Banach algebras Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-27 Fei Peng, Xiaoxiang Zhang
This paper describes the common properties of elements a and b satisfying \(ab^n = b^{n + 1}\) and \(ba^n = a^{n + 1}\) in the settings of Banach algebras, rings and operator algebras from the viewpoint of generalized inverses and spectral theory, where n is a positive integer. As applications, we show that if $$\begin{aligned} M_0 = \begin{pmatrix} T &{} 0 \\ 0 &{} N_0 \end{pmatrix}, M_1 = \begin{pmatrix}
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Two weight estimates for $$L^{r}$$ -Hörmander singular integral operators and rough singular integral operators with matrix weights Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-27 Yongming Wen, Wenting Hu, Fuli Ku
In this paper, we give new bump conditions for two matrix weight inequalities of \(L^{r}\)-Hörmander singular integral operators and rough singular integral operators, which are new even in the scalar cases. As applications, we obtain quantitative one weight inequalities for rough singular integral operators.
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Making more approximate oblique dual frame pairs Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-25 Yun-Zhang Li, Li-Juan Wu
The concept of approximate oblique dual frame was introduced by Díaz, Heineken and Morillas. It is more general than traditional dual frame, oblique dual frame, and approximate dual frame. This paper addresses constructing more approximate oblique dual frame pairs starting from one given oblique dual frame pair. Using “analysis and synthesis operator”, “portrait”, and “gap” perturbation techniques
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Composition operators on weighted Fock spaces induced by $$A_{\infty }$$ -type weights Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-23 Jiale Chen
In this paper, we study the composition operators \(C_{\varphi }\) acting on the weighted Fock spaces \(F^p_{\alpha ,w}\), where w is a weight satisfying some restricted \(A_{\infty }\)-conditions. We first characterize the boundedness and compactness of the composition operators \(C_{\varphi }:F^p_{\alpha ,w}\rightarrow F^q_{\beta ,v}\) for all \(0q\) is also obtained. Then, in the case that \(w(z)=(1+|z|)^{mp}\)
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p-Compactness of Bloch maps Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-21 A. Jiménez-Vargas, D. Ruiz-Casternado
Influenced by the concept of a p-compact operator due to Sinha and Karn (Stud Math 150(1): 17–33, 2002), we introduce p-compact Bloch maps of the open unit disk \(\mathbb {D}\subseteq \mathbb {C}\) to a complex Banach space X, and obtain its most outstanding properties: surjective Banach ideal property, Möbius invariance, linearisation on the Bloch-free Banach space over \(\mathbb {D}\), inclusion
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Cyclic vectors in Fock-type spaces in multi-variable case Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-19 Hansong Huang, Kou Hei Izuchi
This manuscript concerns with cyclic vectors in the Fock-type spaces \({L^{p}_{a}}(\mathbb C^d,s,\alpha )\) of multi-variable cases, with positive parameters \(s,\alpha \) and \(p\ge 1\). The one-variable case has been settled by the authors. Here, it is shown that for a positive number \(s\not \in \mathbb {N}\), a function f in the Fock-type space \({L^{p}_{a}}(\mathbb C^d,s,\alpha )\) is cyclic if
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Regularity results for classes of Hilbert C*-modules with respect to special bounded modular functionals Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-17 Michael Frank
Considering the deeper reasons of the appearance of a remarkable counterexample by Kaad and Skeide (J Operat Theory 89(2):343–348, 2023) we consider situations in which two Hilbert C*-modules \(M \subset N\) with \(M^\bot = \{ 0 \}\) over a fixed C*-algebra A of coefficients cannot be separated by a non-trivial bounded A-linear functional \(r_0: N \rightarrow A\) vanishing on M. In other words, the
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On creating new essential spectrum by self-adjoint extension of gapped operators Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-16 Alessandro Michelangeli
Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily prescribed portions of the gap as essential spectrum are identified and constructed within a general extension scheme. The emergence of new spectrum in the gap by self-adjoint extension is a problem with a long history and recent deep understanding, and
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Lipschitz continuity of the dilation of Bloch functions on the unit ball of a Hilbert space and applications Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-13 Alejandro Miralles
Let \(B_E\) be the open unit ball of a complex finite- or infinite-dimensional Hilbert space. If f belongs to the space \(\mathcal {B}(B_E)\) of Bloch functions on \(B_E\), we prove that the dilation map given by \(x \mapsto (1-\Vert x\Vert ^2) \mathcal {R}f(x)\) for \(x \in B_E\), where \(\mathcal {R}f\) denotes the radial derivative of f, is Lipschitz continuous with respect to the pseudohyperbolic
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Lorentz spaces depending on more than two parameters Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-02-08 Albrecht Pietsch
For more than 50 years, the author has asked himself why Lorentz spaces are only defined for two parameters. Has this choice been made just for simplicity or is it a natural bound that cannot be exceeded? This question is principal and has nothing to do with usefulness. Now, I discovered a way to produce Lorentz sequence spaces for any finite number of parameters. Having found the right approach, everything
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Spectral enclosures for some unbounded $$n\times n$$ operator matrices Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-01-31 Yaru Qi, Yuying Li, Yihui Kong
In this paper, we establish the enclosures for the spectrum of unbounded \(n\times n\) operator matrices in a Banach space. For diagonally dominant and off-diagonally dominant operator matrices, we present a new Gershgorin-type results on the localization of the spectrum by using the Schur complements and the quadratic complements, respectively, that no longer requires dominance order of 0 nor \(<1\)
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A note on commutator-simple algebras Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-01-25 Jiankui Li, Shaoze Pan, Cangyuan Wang
We investigate the property of commutator-simplicity in algebras from both algebraic and analytic perspectives. We demonstrate that a large class of algebras possess this property. As an analytic analog, we introduce the concept of topological commutator-simplicity for Banach algebras and establish that a \(\sigma \)-unital \(C^{*}\)-algebra is topological commutator-simple if and only if its multiplier
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Lie derivable maps on nest algebras Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-01-25 Lei Liu, Kaipeng Li
Let \(\mathcal {N}\) be a non-trivial nest on a Hilbert space H and \(\textrm{alg}\mathcal {N}\) be the associated nest algebra. Let \(G\in \textrm{alg}\mathcal {N}\) be an operator with \(\overline{\textrm{ran}(G)}\in \mathcal {N}\backslash \{H\}\). In this note, we give a description of Lie derivable maps and generalized Lie 2-derivable maps at G of nest algebra \(\textrm{alg}\mathcal {N}\).
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Fredholm properties of a class of coupled operator matrices and their applications Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-01-18
Abstract This paper deals with Fredholm properties of the one-sided coupled operator matrix \({\mathcal {M}}=\left( \begin{array}{cc} A &{} B \\ 0 &{} D \end{array} \right) \left( \begin{array}{cc} I &{} 0 \\ L &{} I \end{array} \right)\) by means of generalized Schur factorization and the associated space decompositions. For \(\lambda \in {\mathbb {C}},\) some sufficient conditions are given for \(\lambda
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Projective and injective tensor products of Banach $$L^0$$ -modules Ann. Funct. Anal. (IF 1.0) Pub Date : 2024-01-08 Enrico Pasqualetto
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Singular value and norm inequalities involving the numerical radii of matrices Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-12-19 Ahmad Al-Natoor, Omar Hirzallah, Fuad Kittaneh
It is shown that if A, B, X, and Y are \(n\times n\) complex matrices, such that X and Y are positive semidefinite, then $$\begin{aligned} s_{j}\left( AXB^{*}+BYA^{*}\right) \le \left( \left\| A\right\| \left\| B\right\| +\omega \left( A^{*}B\right) \right) s_{j}\left( X\oplus Y\right) \end{aligned}$$ for \(j=1,2,\ldots ,n\), and if A is accretive–dissipative, then $$\begin{aligned} \left| \left| \left|
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On the smoothness of normed spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-12-16 Józef Banaś, Justyna Ochab, Tomasz Zając
The aim of the paper is to discuss and clarify some concepts of the geometric theory of normed spaces. We mainly intend to present recent results concerning the concept of smoothness of normed spaces in connection with the concepts of the strict and uniform convexity of those spaces.
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Cesàro-like operators between the Bloch space and Bergman spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-12-09 Yuting Guo, Pengcheng Tang, Xuejun Zhang
Let \({\mathbb {D}}\) be the unit disc in the complex plane. Given a positive finite Borel measure \(\mu \) on the radius [0, 1), we denote the n-th moment of \(\mu \) as \(\mu _{n}\), that is, \(\mu _{n}=\int _{[0,1)}t^{n} \textrm{d}\mu (t).\) The Cesàro-like operator \({\mathcal {C}}_{\mu ,s}\) is defined on \(H({\mathbb {D}})\) as follows: If \(f(z)=\sum _{n=0}^{\infty }a_{n}z^{n} \in H({\mathbb
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Variations of the James and Schäffer constants in Banach spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-12-05 Horst Martini, Pier Luigi Papini, Senlin Wu
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The pseudo-regularity of the range of orthogonal projections in Krein spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-11-22 Lulu Zhang, Guojun Hai
Let P, Q be two orthogonal projections and J be a symmetry such that \(JP=QJ\). Based on the block operator technique and Halmos’ CS decomposition, we devote to characterizing the pseudo-regularity of \({\mathcal {R}}(P)\) and \({\mathcal {R}}(Q)\). It is given the J-projection onto a regular complement of \({\mathcal {R}}(P)^{\circ }\) in \({\mathcal {R}}(P)\) (resp. \({\mathcal {R}}(Q)^{\circ }\)
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Positive periodic solutions for certain kinds of delayed q-difference equations with biological background Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-11-14 Marko Kostić, Halis Can Koyuncuoğlu, Youssef N. Raffoul
This paper specifically focuses on a specific type of q-difference equations that incorporate multiple delays. The main objective is to explore the existence of positive periodic solutions using coincidence degree theory. Notably, the equation studied in this paper has relevance to important biological growth models constructed on quantum domains. The significance of this research lies in the fact
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Genuine Bernstein–Durrmeyer type operators preserving 1 and $$x^j$$ Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-10-28 Ulrich Abel, Ana Maria Acu, Margareta Heilmann, Ioan Raşa
We introduce a family of genuine Bernstein–Durrmeyer type operators preserving the functions 1 and \(x^j\). For them, we establish Voronovskaja type formulas. The behaviour with respect to generalized convex functions is investigated.
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Fixed Point Theorem: variants, affine context and some consequences Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-10-24 Anderson L. A. de Araujo, Edir J. F. Leite
In this work, we will present variants Fixed Point Theorem for the affine and classical contexts, as a consequence of general Brouwer’s Fixed Point Theorem. For instance, the affine results will allow working on affine balls, which are defined through the affine \(L^{p}\) functional \(\mathcal {E}_{p,\Omega }^p\) introduced by Lutwak et al. (J Differ Geom 62:17–38, 2002) for \(p > 1\) that is non convex
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Some properties of the extremal function for the Fuglede p-modulus Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-10-24 Małgorzata Ciska-Niedziałomska
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Estimates for bilinear generalized fractional integral operator and its commutator on generalized Morrey spaces over RD-spaces Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-10-18 Guanghui Lu, Shuangping Tao, Miaomiao Wang
Let \((X,d,\mu )\) be an RD-space. In this paper, we prove that a bilinear generalized fractional integral \(\widetilde{T}_{\alpha }\) is bounded from the product of generalized Morrey spaces \(\mathcal {L}^{\varphi _{1},p_{1}}(X)\times \mathcal {L}^{\varphi _{2},p_{2}}(X)\) into spaces \(\mathcal {L}^{\varphi ,q}(X)\), and it is also bounded from the product of spaces \(\mathcal {L}^{\varphi _{1}
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Beurling quotient subspaces for covariant representations of product systems Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-10-04 Azad Rohilla, Harsh Trivedi, Shankar Veerabathiran
Let \((\sigma , V^{(1)}, \dots , V^{(k)})\) be a pure doubly commuting isometric representation of the product system \({\mathbb {E}}\) on a Hilbert space \({\mathcal {H}}_{V}.\) A \(\sigma \)-invariant subspace \({\mathcal {K}}\) is said to be Beurling quotient subspace of \({\mathcal {H}}_{V}\) if there exist a Hilbert space \({\mathcal {H}}_W,\) a pure doubly commuting isometric representation \((\pi
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On the Schauder fixed point property II Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-09-21 Khadime Salame
The Schauder fixed point property (F) was introduced and studied by Lau and Zhang as a semigroup formulation in the general setting of convex spaces of the well-known Schauder fixed point theorem in Banach spaces. What amenability property should possess a semigroup or a topological group to satisfy the Schauder fixed point property. Recently, the author provided a partial answer to that question and
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A non-trivial solution for a p-Schrödinger–Kirchhoff-type integro-differential system by non-smooth techniques Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-09-18 Juan Mayorga-Zambrano, Daniel Narváez-Vaca
We consider the integro-differential system \((\textrm{P}_m)\): $$\begin{aligned} - \left( a_k+b_k \left( \displaystyle \int _{{\mathbb {R}}^{N}} |\nabla u_k|^{p} dx \right) ^{p-1} \right) \Delta _{p} u_k + V(x) |u_k|^{p-2} u_k = \partial _{k} F(u_1,\ldots ,u_m), \end{aligned}$$ where \(x\in {\mathbb {R}}^N\), \(a_k>0\), \(b_k\ge 0\), \(N\ge 2\) and \(10\) and a coercivity property introduced by Bartsch
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Preduals of variable Morrey–Campanato spaces and boundedness of operators Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-08-31 Ciqiang Zhuo
Let \(p(\cdot ):\ {\mathbb {R}}^n\rightarrow (1,\infty )\) be a variable exponent, such that the Hardy–Littlewood maximal operator is bounded on the variable exponent Lebesgue space \(L^{p(\cdot )}({\mathbb {R}}^n),\) and \(\phi :\ {\mathbb {R}}^n\times (0,\infty )\rightarrow (0,\infty )\) be a function satisfying some conditions. In this article, we give some properties of variable Campanato spaces
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Refinements of the Cauchy–Schwarz inequality in pre-Hilbert $$C^*$$ -modules and their applications Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-08-27 Ali Zamani
New extensions of the Cauchy–Schwarz inequality in the framework of pre-Hilbert \(C^*\)-modules are given. An application to the numerical radius in \(C^*\)-algebras is also provided.
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Rough Hausdorff operators on Lebesgue spaces with variable exponent Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-08-23 Ziwei Li, Jiman Zhao
In this paper, we study rough Hausdorff operators on variable exponent Lebesgue spaces in the setting of the Heisenberg group. We prove the boundedness of rough Hausdorff operators by giving some sufficient conditions.
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Weighted holomorphic mappings attaining their norms Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-08-22 A. Jiménez-Vargas
Given an open subset U of \({\mathbb {C}}^n,\) a weight v on U and a complex Banach space F, let \(\mathcal {H}_v(U,F)\) denote the Banach space of all weighted holomorphic mappings \(f:U\rightarrow F,\) under the weighted supremum norm \(\left\| f\right\| _v:=\sup \left\{ v(z)\left\| f(z)\right\| :z\in U\right\} .\) We prove that the set of all mappings \(f\in \mathcal {H}_v(U,F)\) that attain their
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Noncommutative Pick–Julia theorems for generalized derivations in Q, Q $$^*$$ and Schatten–von Neumann ideals of compact operators Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-08-21 Danko R. Jocić
If C and D are strictly accretive operators on \({\mathcal {H}}\) and at least one of them is normal, such that \(CX\!-\!XD\in { {{{\varvec{{\mathcal {C}}}}}}_{\Psi }({\mathcal {H}})}\) for some \(X\in { {{{\varvec{{\mathcal {B}}}}}}({\mathcal H})}\) and \(Q^*\) symmetrically norming function \(\Psi ,\) then for all holomorphic functions h, mapping the open right half (complex) plane into itself, we
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A note on exceptional sets in Erdös–Rényi limit theorem Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-08-14 Chuntai Liu
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2-Local isometries on vector-valued differentiable functions Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-08-08 Lei Li, Siyu Liu, Weiyun Ren
Let Q, K be connected open subsets of \(\mathbb {R}^m\) and A(X), A(Y) be some kind of function spaces. We will study the 2-local isometries between the vector-valued differentiable function spaces \(C_0^p(Q, A(X))\) and \(C_0^p(K, A(Y))\), and show that they can be written as weighted composition operators.
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Catalan generating functions for bounded operators Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-07-27 Pedro J. Miana, Natalia Romero
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On the positively limited p-Schur property in Banach lattices Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-07-23 Halimeh Ardakani, Khadijeh Amjadi
This paper is devoted to three properties of Banach lattices related to positively limited sets, which are called the positively limited Schur property of order p \((1 \le p \le \infty );\) that is, spaces on which every weakly p-compact and positively limited set is relatively compact, the positive DP\(^*\) property of order p and the weak positively limited Schur property of order p, respectively
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Toms–Winter conjecture for C*-modules Ann. Funct. Anal. (IF 1.0) Pub Date : 2023-07-13 Azam Yousefi, Mohammad R. Mardanbeigi, Massoud Amini
We prove a module version of Toms–Winter conjecture for a class of \(C^*\)-algebras which are \(C^*\)-modules on another \(C^*\)-algebra with compatible actions.