Spectral flow and Dixmier traces
Date
2003
Authors
Carey, Alan
Phillips, John
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 heat operator in a general semi-finite von Neumann algebra. Our results have several applications. We deduce a formula for the Chern character of an odd ℒ(1,∞)-summable Breuer-Fredholm module in terms of a Hochschild 1-cycle. We explain how to derive a Wodzicki residue for pseudo-differential operators along the orbits of an ergodic Rn action on a compact space X. Finally, we give a short proof of an index theorem of Lesch for generalised Toeplitz operators.
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Keywords: L (p,8)-summable Fredholm module; Dixmier trace; Spectral flow; Zeta function
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Source
Advances in Mathematics
Type
Journal article
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Restricted until
2037-12-31
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