The Schur-Horn theorem for operators with three point spectrum

TL;DR

This paper establishes a Schur-Horn theorem for self-adjoint operators with three-point spectra, characterizing their diagonals within the unitary orbit, extending classical results to a specific spectral case.

Contribution

It provides a novel Schur-Horn theorem for operators with three-point spectrum, generalizing Kadison's result for orthogonal projections.

Findings

Characterization of diagonals for operators with three-point spectrum

Extension of Schur-Horn theorem to a new class of operators

Analogous results to Kadison's theorem for this spectral case

Abstract

We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with three points in the spectrum. Our result gives a Schur-Horn theorem for operators with three point spectrum analogous to Kadison's result for orthogonal projections.