The Schur-Horn theorem for operators with finite spectrum

TL;DR

This paper extends the classical Schur-Horn theorem to infinite-dimensional Hilbert spaces for self-adjoint operators with finite spectrum, generalizing previous results for projections and three-point spectrum operators.

Contribution

It provides a characterization of diagonals of operators with finite spectrum in infinite-dimensional spaces, expanding the scope of the Schur-Horn theorem.

Findings

Characterization of diagonals of self-adjoint operators with finite spectrum

Extension of Schur-Horn theorem to infinite-dimensional setting

Connection to Kadison's theorem and previous spectral results

Abstract

We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with a finite spectrum. 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.