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Transactions of the American Mathematical Society

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Trace class self-commutators

Authors: C. A. Berger and Marion Glazerman Ben-Jacob
Journal: Trans. Amer. Math. Soc. 277 (1983), 75-91
MSC: Primary 47C15; Secondary 46L10, 47B20
MathSciNet review: 690041
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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 $.

References [Enhancements On Off] (What's this?)

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Keywords: Normal trace, $ {W^\ast}$-algebra, von Neumann algebra, hyponormal operator, self-commutator
Article copyright: © Copyright 1983 American Mathematical Society

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