The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Journal of Spectral Theory


Full-Text PDF (339 KB) | Metadata | Table of Contents | JST summary
Volume 6, Issue 1, 2016, pp. 1–41
DOI: 10.4171/JST/116

Published online: 2016-04-04

Universal measurability and the Hochschild class of the Chern character

Alan L. Carey[1], Adam Rennie[2], Fedor Sukochev[3] and Dmitriy Zanin[4]

(1) The Australian National University, Canberra, Australia
(2) University of Wollongong, Australia
(3) University of New South Wales, Sydney, Australia
(4) University of New South Wales, Sydney, Australia

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 $\mathcal A, H, D$ and Hochschild cycles for $\mathcal A$.

Keywords: Singular trace, operator ideal, measurability, Chern character, spectral triple

Carey Alan, Rennie Adam, Sukochev Fedor, Zanin Dmitriy: Universal measurability and the Hochschild class of the Chern character. J. Spectr. Theory 6 (2016), 1-41. doi: 10.4171/JST/116