Nearest normal approximation for certain operators
John D. Phillips · Proceedings of the American Mathematical Society · 1977
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.