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The Dixmier trace and asymptotics of zeta functions

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


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.

CollectionsANU Research Publications
Date published: 2007
Type: Journal article
Source: Journal of Functional Analysis
DOI: 10.1016/j.jfa.2007.04.011


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