The Schur-Horn theorem for operators with three point spectrum

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 Pythagorean theorem and carpenter's theorem, which characterize the diagonals of orthogonal projections. (C) 2013 Elsevier Inc. All rights reserved.