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A characterization of Gibbs semigroups

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Abstract

We propose a new characterization of Gibbs semigroups, which is an extension of a similar characterization for compact semigroups.

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References

  1. E. Hille and R. S. Phillips, “Functional Analysis and Semi-Groups,” (American Mathematical Society Colloquium Publications, Vol. 31), Amer. Math. Soc., Providence, RI (1957).

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  2. E. B. Davies, Linear Operators and their Spectra (Cambridge Studies in Advanced Mathematics, Vol. 106), Cambridge Univ. Press, Cambridge (2007).

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  4. M. Eckstein and B. Iochum, Spectral Action in Noncommutative Geometry (Springer Briefs in Mathematical Physics, Vol. 27), Springer, Cham (2018).

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  5. B. Iochum and V. A. Zagrebnov, “Asymptotic behaviour of semigroup traces and Schatten classes of resolvents,” arXiv: 2309.05394.

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Acknowledgments

This paper is motivated by a talk given by V. A. Zagrebnov at the International conference dedicated to the 100th anniversary of the birthday of V. S. Vladimirov (January 9–14, 2023, Steklov Mathematical Institute, Moscow). He is thankful to the Organizing Committee and the Chair Professor Igor Volovich for the idea to deliver this talk. Both authors are grateful for the invitation to submit a contribution for publication in “Theoretical and Mathematical Physics.”

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Institut de Mathématiques de Marseille — CMI, Université d’Aix-Marseille, CNRS, Marseille, France

    V. A. Zagrebnov

  2. Centre de Physique Théorique, Université d’Aix-Marseille, Université de Toulon, CNRS, Marseille, France

    B. Iochum

Authors
  1. V. A. Zagrebnov
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  2. B. Iochum
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Corresponding author

Correspondence to V. A. Zagrebnov.

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The authors of this work declare that they have no conflicts of interest.

Additional information

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, 2024, Vol. 218, pp. 88–101 https://doi.org/10.4213/tmf10540.

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Zagrebnov, V.A., Iochum, B. A characterization of Gibbs semigroups. Theor Math Phys 218, 75–86 (2024). https://doi.org/10.1134/S0040577924010069

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  • DOI: https://doi.org/10.1134/S0040577924010069

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