Universal measurability and the Hochschild class of the Chern character
Alan L. Carey
The Australian National University, Canberra, AustraliaAdam Rennie
University of Wollongong, AustraliaFedor Sukochev
University of New South Wales, Sydney, AustraliaDmitriy Zanin
University of New South Wales, Sydney, Australia
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Abstract
We study notions of measurability for singular traces, and characterise universal measurability for operators in Dixmier ideals. This measurability result is then applied to improve on the various proofs of Connes’ identication of the Hochschild class of the Chern character of Dixmier summable spectral triples.
The measurability results show that the identication of the Hochschild class is independent of the choice of singular trace. As a corollary we obtain strong information on the asymptotics of the eigenvalues of operators naturally associated to spectral triples and Hochschild cycles for .
Cite this article
Alan L. Carey, Adam Rennie, Fedor Sukochev, Dmitriy Zanin, Universal measurability and the Hochschild class of the Chern character. J. Spectr. Theory 6 (2016), no. 1, pp. 1–41
DOI 10.4171/JST/116