The Dixmier trace and asymptotics of zeta functions

Authors

Alan L. Carey, Australian National University
Adam C. Rennie, University of CopenhagenFollow
Aleksandr Sedaev, Voronezh State University Of Architecture And Construction
Fyodor A. Sukochev, Flinders University

RIS ID

77530

Publication Details

Carey, A. L., Rennie, A. C., Sedaev, A. & Sukochev, F. A. (2007). The Dixmier trace and asymptotics of zeta functions. Journal of Functional Analysis, 249 (2), 253-283.

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.