Finite and infinite dimensional generalizations of Klyachko's theorem

Abstract

We describe the convex set of the eigenvalues of Hermitian matrices which are majorized by a sum of m Hermitian matrices with prescribed eigenvalues. We extend our characterization to selfadjoint nonnegative (definite) compact operators on a separable Hilbert space. We give necessary and sufficient conditions on the eigenvalue sequence of a selfadjoint nonnegative compact operator of trace class to be a sum of m selfadjoint nonnegative compact operators of trace class with prescribed eigenvalue sequences.