Diagonals of Self-adjoint Operators with Finite Spectrum
Volume 63 / 2015
Bulletin Polish Acad. Sci. Math. 63 (2015), 249-260
MSC: Primary 42C15, 47B15; Secondary 46C05.
DOI: 10.4064/ba8024-12-2015
Published online: 18 December 2015
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 (2002) and the second author’s result for operators with three-point spectrum (2013).
