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Spectral flow and Dixmier traces

Alan L Carey·John Phillips·Fyodor Sukochev
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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 heat operator in a general semi-finite von Neumann algebra. Our results have several applications. We deduce a formula for the Chern character of an odd ${\mathcal L}^{(1,\infty)}$-summable Breuer-Fredholm module in terms of a Hochschild 1-cycle. We explain how to derive a Wodzicki residue for pseudo-differential operators along the orbits of an ergodic $\IR^n$ action on a compact space $X$. Finally we give a short proof an index theorem of Lesch for generalised Toeplitz operators.

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Alan L Carey, John Phillips, Fyodor Sukochev. 2002-05-08. Spectral flow and Dixmier traces. https://arxiv.org/abs/math/0205076

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