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Some characterizations of Hermitian operators and related classes of operators. I


Authors: Che Kao Fong and Vasile I. Istrăţescu
Journal: Proc. Amer. Math. Soc. 76 (1979), 107-112
MSC: Primary 47B20
DOI: https://doi.org/10.1090/S0002-9939-1979-0534398-X
MathSciNet review: 534398
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Abstract: It is shown that, among other things, an operator T is hermitian if and only if $ \vert T{\vert^2} \leqslant {(\operatorname{Re} T)^2}$. Also, the class of those operators T satisfying $ \vert T{\vert^2} \geqslant {(\operatorname{Re} T)^2}$ is investigated.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0534398-X
Keywords: Hermitian operator, hyponormal operator, real part of an operator, class (WN), spectrum
Article copyright: © Copyright 1979 American Mathematical Society