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Diagonals of Self-adjoint Operators with Finite Spectrum

Volume 63 / 2015

Marcin Bownik, John Jasper 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


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).


  • Marcin BownikDepartment of Mathematics
    University of Oregon
    Eugene, OR 97403-1222, U.S.A.
  • John JasperDepartment of Mathematical Sciences
    University of Cincinnati
    Cincinnati, OH 45221-0025, U.S.A.

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