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The Dixmier trace and asymptotics of zeta functions |
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| Authors: | Alan L Carey Adam Rennie Aleksandr Sedaev Fyodor Sukochev |
| Institution: | a Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia b Institute for Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark c Department of Mathematics, Voronezh State University of Architecture and Construction, 20-letiya Oktyabrya 84, Voronezh 394006, Russia d School of Informatics and Engineering, Flinders University, Bedford Park 5042, Australia |
| 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. |
| Keywords: | Spectral triple Dixmier trace Zeta function |
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