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arXiv · 2309.05394

Asymptotic Behaviour of Semigroup Traces and Schatten Classes of Resolvents

Bruno Iochum·Valentin A. Zagrebnov
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Abstract

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.

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Bruno Iochum, Valentin A. Zagrebnov. 2023-09-11. Asymptotic Behaviour of Semigroup Traces and Schatten Classes of Resolvents. https://doi.org/10.1016/j.jfa.2025.111101

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