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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Nearest normal approximation for certain operators

Author: John Phillips
Journal: Proc. Amer. Math. Soc. 67 (1977), 236-240
MSC: Primary 47A55; Secondary 47B20
MathSciNet review: 0458212
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Abstract: In this paper we show that binormal operators have nearest normal approximants. In fact, we exhibit nearest normals to such operators and, as a corollary, show that the hermitian part of a binormal operator with real spectrum is a nearest normal. We obtain further corollaries on nearest normal approximation to operators which are square roots of normal operators and then apply these results to perturbations of operator algebras.

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Keywords: Normal operator, binormal operator, normal approximation, perturbations of operator algebras
Article copyright: © Copyright 1977 American Mathematical Society