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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some trace class commutators of trace zero

Author: Fuad Kittaneh
Journal: Proc. Amer. Math. Soc. 113 (1991), 655-661
MSC: Primary 47B47; Secondary 47B10
MathSciNet review: 1086332
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Abstract: It is shown that if $ T$ is an operator on a separable complex Hilbert space and $ X$ is a Hilbert-Schmidt operator such that $ TX - XT$ is a trace class operator, then the trace of $ TX - XT$ is zero provided one of the two conditions holds: (a) $ {T^2}$ is normal; (b) $ {T^n}$ is normal for some integer $ n > 2$ and $ {T^*}T - T{T^*}$ is a trace class operator. Related results involving essentially unitary operators and Cesàro operators are also given.

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Keywords: Commutator, compact operator, Hilbert-Schmidt operator, trace, trace class, Schatten $ p$-class, normal operator, selfadjoint operator, essentially unitary operator, Cesàro operator
Article copyright: © Copyright 1991 American Mathematical Society