Journal of Noncommutative Geometry


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Volume 8, Issue 2, 2014, pp. 321–336
DOI: 10.4171/JNCG/158

Published online: 2014-07-18

Dixmier traces generated by exponentiation invariant generalised limits

Fedor Sukochev[1], Alexandr Usachev[2] and Dmitriy Zanin[3]

(1) University of New South Wales, Sydney, Australia
(2) University of New South Wales, Sydney, Australia
(3) University of New South Wales, Sydney, Australia

We define a new class of singular positive traces on the ideal $\mathcal{M}_{1,\infty}$ of $B(H)$ generated by exponentiation invariant generalized limits. We prove that this new class is strictly contained in the class of all Dixmier traces. We also prove a Lidskii-type formula for this class of traces.

Keywords: Dixmier traces, measurable elements, exponentiation invariant generalized limits, Lidskii formula

Sukochev Fedor, Usachev Alexandr, Zanin Dmitriy: Dixmier traces generated by exponentiation invariant generalised limits. J. Noncommut. Geom. 8 (2014), 321-336. doi: 10.4171/JNCG/158