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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 $.

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

  • [1] P. Fan, On the diagonal of an operator, Trans. Amer. Math. Soc. 283 (1984), 239-251. MR 735419 (86b:47034)
  • [2] P. Fan, C.-K. Fong, and D. A. Herrero, On zero-diagonal operators and traces, Proc. Amer. Math. Soc. 99 (1987), 445-451. MR 875378 (88c:47009)
  • [3] P. R. Halmos, Finite-dimensional vector spaces, Van Nostrand, Princeton, NJ, 1958. MR 0089819 (19:725b)

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Keywords: Zero diagonal operators, trace, trace-class operators
Article copyright: © Copyright 1994 American Mathematical Society

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