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

Fong, Che Kao; Istrăţescu, Vasile I.

doi:10.1090/S0002-9939-1979-0534398-X

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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