Some trace class commutators of trace zero
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- by Fuad Kittaneh PDF
- Proc. Amer. Math. Soc. 113 (1991), 655-661 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 655-661
- MSC: Primary 47B47; Secondary 47B10
- DOI: https://doi.org/10.1090/S0002-9939-1991-1086332-X
- MathSciNet review: 1086332