Extended zeta-function residues on principal ideals
Functional Analysis
2024-07-09 v1
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.
Keywords
Cite
@article{arxiv.2407.05296,
title = {Extended zeta-function residues on principal ideals},
author = {Yongqiang Tian and Alexandr Usachev},
journal= {arXiv preprint arXiv:2407.05296},
year = {2024}
}