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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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 $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0690041-6
PII: S 0002-9947(1983)0690041-6
Keywords: Normal trace, $ {W^\ast}$-algebra, von Neumann algebra, hyponormal operator, self-commutator
Article copyright: © Copyright 1983 American Mathematical Society