INTEGRAL OPERATORS ASSOCIATED WITY THE GENERALIZED FUGLEDE PROPERTY

Jingbo Xia

doi:10.7900/jot.2021dec12.2367

INTEGRAL OPERATORS ASSOCIATED WITY THE GENERALIZED FUGLEDE PROPERTY

Jingbo Xia

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a class of integral operators T_K,μ that arise from various problems studied in the past, one of which is the generalized Fuglede commutation property. We show that under a rather general growth condition on the measure μ, the operator T_K,μ belongs to the Lorentz ideal C⁺₁. This naturally leads to the challenge of computing the Dixmier trace of T_K,μ. In the case where μ is the restriction of the Lebesgue measure m_n to a bounded Borel set in Rⁿ, we show that the Dixmier trace of T_K,μ is 0.

Original language	English
Pages (from-to)	401-423
Number of pages	23
Journal	Journal of Operator Theory
Volume	90
Issue number	2
DOIs	https://doi.org/10.7900/jot.2021dec12.2367
State	Published - 2023

Keywords

Dixmier trace
Fuglede property
integral operator

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10.7900/jot.2021dec12.2367

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title = "INTEGRAL OPERATORS ASSOCIATED WITY THE GENERALIZED FUGLEDE PROPERTY",

abstract = "We consider a class of integral operators TK,μ that arise from various problems studied in the past, one of which is the generalized Fuglede commutation property. We show that under a rather general growth condition on the measure μ, the operator TK,μ belongs to the Lorentz ideal C+1. This naturally leads to the challenge of computing the Dixmier trace of TK,μ. In the case where μ is the restriction of the Lebesgue measure mn to a bounded Borel set in Rn, we show that the Dixmier trace of TK,μ is 0.",

keywords = "Dixmier trace, Fuglede property, integral operator",

author = "Jingbo Xia",

note = "Publisher Copyright: {\textcopyright} Copyright by THETA, 2023",

year = "2023",

doi = "10.7900/jot.2021dec12.2367",

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N2 - We consider a class of integral operators TK,μ that arise from various problems studied in the past, one of which is the generalized Fuglede commutation property. We show that under a rather general growth condition on the measure μ, the operator TK,μ belongs to the Lorentz ideal C+1. This naturally leads to the challenge of computing the Dixmier trace of TK,μ. In the case where μ is the restriction of the Lebesgue measure mn to a bounded Borel set in Rn, we show that the Dixmier trace of TK,μ is 0.

AB - We consider a class of integral operators TK,μ that arise from various problems studied in the past, one of which is the generalized Fuglede commutation property. We show that under a rather general growth condition on the measure μ, the operator TK,μ belongs to the Lorentz ideal C+1. This naturally leads to the challenge of computing the Dixmier trace of TK,μ. In the case where μ is the restriction of the Lebesgue measure mn to a bounded Borel set in Rn, we show that the Dixmier trace of TK,μ is 0.

KW - Dixmier trace

KW - Fuglede property

KW - integral operator

UR - https://www.scopus.com/pages/publications/85174692265

U2 - 10.7900/jot.2021dec12.2367

DO - 10.7900/jot.2021dec12.2367

M3 - Article

AN - SCOPUS:85174692265

SN - 0379-4024

VL - 90

SP - 401

EP - 423

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 2

ER -

INTEGRAL OPERATORS ASSOCIATED WITY THE GENERALIZED FUGLEDE PROPERTY

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