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arXiv · 1311.0937

Which traces are spectral?

F. Sukochev·D. Zanin
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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.

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F. Sukochev, D. Zanin. 2013-11-05. Which traces are spectral?. https://arxiv.org/abs/1311.0937

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