Diagonals of self-adjoint operators with finite spectrum

Abstract

Given a finite set $X\subseteq \mathbb{R}$ we characterize the diagonals of self-adjoint operators with spectrum $X$. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections and the second author's result for operators with three point spectrum.

arXiv commentarXiv admin note: text overlap with arXiv:1302.4757