The Dixmier trace and asymptotics of zeta functions

By Alan L. Carey, A. Rennie, A. Sedaev, F. Sukochev. 2006

73 citations recorded by the source corpus.

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 L p , ∞ on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/be9a4b46d861da02efa516cd6fa34f67390ba929

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In Algebra and Number Theory

1. D. Potapov
2. Fedor Sukochev
3. Alan L. Carey

In Mathematical Physics

1. D. Potapov
2. Fedor Sukochev
3. Alan L. Carey
4. V. Peller

Citations in the corpus

• Unbounded Fredholm modules and double operator integrals (2008, methodology): “This result is further used to show continuous differentiability of the mapping between an odd E-summable spectral triple and its bounded counterpart.”