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Measurable operators and the asymptotics of heat kernels and zeta functions
Authors:Alan Carey  Fedor Sukochev
Institution:1. Mathematical Sciences Institute, Australian National University, Canberra ACT, 0200, Australia;2. School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia
Abstract:In this note we answer some questions inspired by the introduction in Connes (1988, 1994) 6], 7] of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of ζ-functions and heat kernels. The answers have remained elusive for some 15 years.
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