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The Dixmier trace and asymptotics of zeta functions

Journal Article


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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.

Publication Date


  • 2007

Citation


  • 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.

Scopus Eid


  • 2-s2.0-34250682687

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1633&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/627

Number Of Pages


  • 30

Start Page


  • 253

End Page


  • 283

Volume


  • 249

Issue


  • 2

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.

Publication Date


  • 2007

Citation


  • 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.

Scopus Eid


  • 2-s2.0-34250682687

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1633&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/627

Number Of Pages


  • 30

Start Page


  • 253

End Page


  • 283

Volume


  • 249

Issue


  • 2