Trace class self-commutators

Berger, C. A.; Ben-Jacob, Marion Glazerman

doi:10.1090/S0002-9947-1983-0690041-6

Trace class self-commutators
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by C. A. Berger and Marion Glazerman Ben-Jacob PDF

Trans. Amer. Math. Soc. 277 (1983), 75-91 Request permission

Abstract:

This paper extends earlier results of Berger and Shaw to all ${W^\ast }$ algebras. The multiplicity of an operator in a ${W^\ast }$ algebra is defined in terms of the trace on the ${W^\ast }$-algebra, and it is shown that if $T$ is a hyponormal operator in such an algebra, the trace of its self-commutator is bounded by this multiplicity times the area of the spectrum of $T$, divided by $\pi$.

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Introduction to Hilbert space and the theory of spectral multiplicity

Trace class self-commutators of hyponormal operators