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Proceedings of the American Mathematical Society

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A characterization of normal operators using the Hilbert-Schmidt class


Author: Ritsuo Nakamoto
Journal: Proc. Amer. Math. Soc. 79 (1980), 343-344
MSC: Primary 47B15; Secondary 47B10
DOI: https://doi.org/10.1090/S0002-9939-1980-0565369-3
MathSciNet review: 565369
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Abstract: A bounded linear operator N on a Hilbert space H is normal if and only if $ \Vert NX - XN\Vert _2 = \Vert N^* X - X N^*\Vert _2$ for every X in the Hilbert-Schmidt class.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0565369-3
Keywords: Hilbert-Schmidt class, normal operator
Article copyright: © Copyright 1980 American Mathematical Society

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