Which traces are spectral?
Operator Algebras
2013-11-06 v1
Abstract
Among ideals of compact operators on a Hilbert space we identify a subclass of those closed with respect to the logarithmic submajorization. Within this subclass, we answer the questions asked by Pietsch \cite{Pietsch_nachrichten} and by Dykema, Figiel, Weiss and Wodzicki \cite{DFWW}. In the first case, we show that Lidskii-type formulae hold for every trace on such ideal. In the second case, we provide the description of the commutator subspace associated with a given ideal. Finally, we prove that a positive trace on an arbitrary ideal is spectral if and only if it is monotone with respect to the logarithmic submajorization.
Keywords
Cite
@article{arxiv.1311.0937,
title = {Which traces are spectral?},
author = {F. Sukochev and D. Zanin},
journal= {arXiv preprint arXiv:1311.0937},
year = {2013}
}