Diagonals of Self-adjoint Operators with Finite Spectrum
نویسندگان
چکیده
منابع مشابه
Diagonals of Self-adjoint Operators with Finite Spectrum
Given a finite set X ⊆ R we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the SchurHorn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to Kadison’s theorem for orthogonal projections [8, 9] and the second author’s result for operators with three point spectrum [7].
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The eigenvalues of a self-adjoint n×n matrix A can be put into a decreasing sequence λ = (λ1, . . . , λn), with repetitions according to multiplicity, and the diagonal of A is a point of R that bears some relation to λ. The Schur-Horn theorem characterizes that relation in terms of a system of linear inequalities. We give a new proof of the latter result for positive trace-class operators on in...
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ژورنال
عنوان ژورنال: Bulletin Polish Acad. Sci. Math.
سال: 2015
ISSN: 0239-7269,1732-8985
DOI: 10.4064/ba8024-12-2015