Asymptotic Behaviour of Semigroup Traces and Schatten Classes of Resolvents

Motivated by examples from physics and noncommutative geometry, given a generator $A$ of a Gibbs semigroup, we reexamine the relationship between the Schatten class of its resolvents and the behaviour of the norm-trace $\norm{e^{-tA}}_1\,$ when $t$ approaches zero. In addition to applying Tauberian...

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Bibliographic Details
Main Authors Iochum, Bruno, Zagrebnov, Valentin A
Format Journal Article
LanguageEnglish
Published 11.09.2023
Subjects
Mathematics - Mathematical Physics
Physics - Mathematical Physics
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Summary:Motivated by examples from physics and noncommutative geometry, given a generator $A$ of a Gibbs semigroup, we reexamine the relationship between the Schatten class of its resolvents and the behaviour of the norm-trace $\norm{e^{-tA}}_1\,$ when $t$ approaches zero. In addition to applying Tauberian results, we specifically investigate the compatibility of asymptotic behaviours with derivations and perturbations. Along the course of our study, we present a novel characterisation of Gibbs semigroups.
DOI:10.48550/arxiv.2309.05394