Measurable operators and the asymptotics of heat kernels and zeta functions

Alan Carey; Fedor Sukochev

doi:10.1016/j.jfa.2012.03.008

Measurable operators and the asymptotics of heat kernels and zeta functions

Alan Carey^*, Fedor Sukochev

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

In this note we answer some questions inspired by the introduction in Connes (1988, 1994) [6,7] of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of ζ-functions and heat kernels. The answers have remained elusive for some 15 years.

Original language	English
Pages (from-to)	4582-4599
Number of pages	18
Journal	Journal of Functional Analysis
Volume	262
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2012.03.008
Publication status	Published - 15 May 2012

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10.1016/j.jfa.2012.03.008

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title = "Measurable operators and the asymptotics of heat kernels and zeta functions",

abstract = "In this note we answer some questions inspired by the introduction in Connes (1988, 1994) [6,7] of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of ζ-functions and heat kernels. The answers have remained elusive for some 15 years.",

keywords = "Ces{\`a}ro operator, Dixmier traces, Generalized limits, Heat kernels, Measurable elements",

author = "Alan Carey and Fedor Sukochev",

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T1 - Measurable operators and the asymptotics of heat kernels and zeta functions

AU - Carey, Alan

AU - Sukochev, Fedor

PY - 2012/5/15

Y1 - 2012/5/15

N2 - In this note we answer some questions inspired by the introduction in Connes (1988, 1994) [6,7] of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of ζ-functions and heat kernels. The answers have remained elusive for some 15 years.

AB - In this note we answer some questions inspired by the introduction in Connes (1988, 1994) [6,7] of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of ζ-functions and heat kernels. The answers have remained elusive for some 15 years.

KW - Cesàro operator

KW - Dixmier traces

KW - Generalized limits

KW - Heat kernels

KW - Measurable elements

UR - https://www.scopus.com/pages/publications/84858797777

U2 - 10.1016/j.jfa.2012.03.008

DO - 10.1016/j.jfa.2012.03.008

M3 - Article

SN - 0022-1236

VL - 262

SP - 4582

EP - 4599

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

ER -

Measurable operators and the asymptotics of heat kernels and zeta functions

Abstract

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