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Singular Traces and Compact Operators. I

S. Albeverio·D. Guido·A. Ponosov·S. Scarlatti
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Abstract

We give a necessary and sufficient condition on a positive compact operator $T$ for the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value on $T$. This generalizes previous results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states on $\ell^\infty(\Bbb N)$ using tools of non standard analysis in an essential way.

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BibTeXRIS

S. Albeverio, D. Guido, A. Ponosov, S. Scarlatti. 1993-08-09. Singular Traces and Compact Operators. I. https://doi.org/10.1006/jfan.1996.0047

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