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Diagonals of Self-adjoint Operators with Finite Spectrum

Bownik M., Jasper J.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

Vol. 63, no. 3

249--260

Given a finite set X ⊆ 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).