An intrinsic characterization for zero-diagonal operators
HTML articles powered by AMS MathViewer
- by Peng Fan and Che Kao Fong PDF
- Proc. Amer. Math. Soc. 121 (1994), 803-805 Request permission
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
- Peng Fan, On the diagonal of an operator, Trans. Amer. Math. Soc. 283 (1984), no. 1, 239–251. MR 735419, DOI 10.1090/S0002-9947-1984-0735419-8
- Peng Fan, Che Kao Fong, and Domingo A. Herrero, On zero-diagonal operators and traces, Proc. Amer. Math. Soc. 99 (1987), no. 3, 445–451. MR 875378, DOI 10.1090/S0002-9939-1987-0875378-9
- Paul R. Halmos, Finite-dimensional vector spaces, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Inc., Princeton-Toronto-New York-London, 1958. 2nd ed. MR 0089819
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 803-805
- MSC: Primary 47A99; Secondary 47B99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1185279-0
- MathSciNet review: 1185279