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arXiv · 2407.05296

Extended zeta-function residues on principal ideals

Yongqiang Tian·Alexandr Usachev
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Abstract

We study extended zeta-function residues on principal ideals of compact operators and their connections with Dixmier traces. We establish a Lidskii-type formula for continuous singular traces on these ideals. Using this formula, we obtain a necessary and sufficient conditions for an arbitrary operator being Dixmier measurable. These conditions are expressed in terms of eigenvalues of an operator and an asymptotic of its zeta-function.

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Yongqiang Tian, Alexandr Usachev. 2024-07-07. Extended zeta-function residues on principal ideals. https://arxiv.org/abs/2407.05296

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