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Integration on locally compact noncommutative spaces

Carey, Alan; Gayral, V.; Rennie, Adam; Sukochev, Fedor A


We present an ab initio approach to integration theory for nonunital spectral triples. This is done without reference to local units and in the full generality of semifinite noncommutative geometry. The main result is an equality between the Dixmier trace and generalised residue of the zeta function and heat kernel of suitable operators. We also examine definitions for integrable bounded elements of a spectral triple based on zeta function, heat kernel and Dixmier trace techniques. We show that...[Show more]

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
Source: Journal of Functional Analysis
DOI: 10.1016/j.jfa.2012.04.015


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