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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An intrinsic characterization for zero-diagonal operators


Authors: Peng Fan and Che Kao Fong
Journal: Proc. Amer. Math. Soc. 121 (1994), 803-805
MSC: Primary 47A99; Secondary 47B99
MathSciNet review: 1185279
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Abstract: The purpose of this paper is to present the following intrinsic characterization for zero-diagonal operators.

Theorem. An operator T has a zero diagonal if and only if $ {\text{tr}}\operatorname{Re} ({e^{i\theta }}) + = {\text{tr}}\operatorname{Re} {({e^{i\theta }}T)_ - }$ for all $ \theta ,0 \leq \theta < 2\pi $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1185279-0
PII: S 0002-9939(1994)1185279-0
Keywords: Zero diagonal operators, trace, trace-class operators
Article copyright: © Copyright 1994 American Mathematical Society