The Dixmier trace and asymptotics of zeta functions

Alan L. Carey; Adam Rennie; Aleksandr Sedaev; Fyodor Sukochev

doi:10.1016/j.jfa.2007.04.011

The Dixmier trace and asymptotics of zeta functions

Alan L. Carey^*, Adam Rennie, Aleksandr Sedaev, Fyodor Sukochev

^*Corresponding author for this work

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

48 Citations (Scopus)

Abstract

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results in a general semi-finite von Neumann algebra. We find for p > 1 that the asymptotics of the zeta function determines an ideal strictly larger than L^{p, ∞} on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions.

Original language	English
Pages (from-to)	253-283
Number of pages	31
Journal	Journal of Functional Analysis
Volume	249
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2007.04.011
Publication status	Published - 15 Aug 2007

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keywords = "Dixmier trace, Spectral triple, Zeta function",

author = "Carey, {Alan L.} and Adam Rennie and Aleksandr Sedaev and Fyodor Sukochev",

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AU - Carey, Alan L.

AU - Rennie, Adam

AU - Sedaev, Aleksandr

AU - Sukochev, Fyodor

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Y1 - 2007/8/15

N2 - We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results in a general semi-finite von Neumann algebra. We find for p > 1 that the asymptotics of the zeta function determines an ideal strictly larger than Lp, ∞ on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions.

AB - We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results in a general semi-finite von Neumann algebra. We find for p > 1 that the asymptotics of the zeta function determines an ideal strictly larger than Lp, ∞ on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions.

KW - Dixmier trace

KW - Spectral triple

KW - Zeta function

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U2 - 10.1016/j.jfa.2007.04.011

DO - 10.1016/j.jfa.2007.04.011

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VL - 249

SP - 253

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

The Dixmier trace and asymptotics of zeta functions

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