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arxiv: 2407.05296 · v1 · pith:3XW7Z7DEnew · submitted 2024-07-07 · 🧮 math.FA

Extended zeta-function residues on principal ideals

Yongqiang Tian , Alexandr Usachev This is my paper
classification 🧮 math.FA
keywords idealszeta-functionconditionsdixmierextendedformulaoperatorprincipal
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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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  1. Nonclassical Weyl laws and Connes' Integration for weak Lorentz ideals, I

    math.OA 2026-05 unverdicted novelty 7.0

    Constructs Dixmier traces via eigenvalue sequences in weak Lorentz ideals, gives spectral characterization of measurable operators answering Connes, and applies to nonclassical Weyl laws.