Nearest normal approximation for certain operators

Phillips, John

doi:10.1090/S0002-9939-1977-0458212-4

Nearest normal approximation for certain operators
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Proc. Amer. Math. Soc. 67 (1977), 236-240 Request permission

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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