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Integration on locally compact noncommutative spaces

Journal Article


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Abstract


  • 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 zeta functions and heat kernels

    yield equivalent notions of integrability, which imply Dixmier traceability.

Publication Date


  • 2012

Citation


  • Carey, A. L., Gayral, V., Rennie, A. & Sukochev, F. A. (2012). Integration on locally compact noncommutative spaces. Journal of Functional Analysis, 263 (2), 383-414.

Scopus Eid


  • 2-s2.0-84861341835

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=9230&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/1895

Number Of Pages


  • 31

Start Page


  • 383

End Page


  • 414

Volume


  • 263

Issue


  • 2

Abstract


  • 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 zeta functions and heat kernels

    yield equivalent notions of integrability, which imply Dixmier traceability.

Publication Date


  • 2012

Citation


  • Carey, A. L., Gayral, V., Rennie, A. & Sukochev, F. A. (2012). Integration on locally compact noncommutative spaces. Journal of Functional Analysis, 263 (2), 383-414.

Scopus Eid


  • 2-s2.0-84861341835

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=9230&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/1895

Number Of Pages


  • 31

Start Page


  • 383

End Page


  • 414

Volume


  • 263

Issue


  • 2