The Dixmier trace and asymptotics of zeta functions

Date

2007

Authors

Carey, Alan
Rennie, Adam Charles
Sedaev, Aleksandr
Sukochev, Fedor A

Journal Title

Journal ISSN

Volume Title

Publisher

Academic Press

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 Lp, ∞ on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions.

Description

Keywords

Keywords: Dixmier trace; Spectral triple; Zeta function

Citation

Source

Journal of Functional Analysis

Type

Journal article

Book Title

Entity type

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License Rights

Restricted until

2037-12-31