The Dixmier trace and asymptotics of zeta functions
Date
2007
Authors
Carey, Alan
Rennie, Adam Charles
Sedaev, Aleksandr
Sukochev, Fedor A
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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.
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Keywords
Keywords: Dixmier trace; Spectral triple; Zeta function
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Source
Journal of Functional Analysis
Type
Journal article
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2037-12-31
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