Congruence of selfadjoint operators

Abstract

Given a bounded selfadjoint operator a in a Hilbert space H, the aim of this paper is to study the orbit of a, i.e., the set of operators which are congruent to a. We establish some necessary and sufficient conditions for an operator to be in the orbit of a. Also, the orbit of a selfadjoint operator with closed range is provided with a structure of differential manifold.