Diagonals of Self-adjoint Operators
نویسندگان
چکیده
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 prove an extension of the latter result for positive trace-class operators on infinite dimensional Hilbert spaces, generalizing results of one of us on the diagonals of projections. We also establish an appropriate counterpart of the Schur inequalities that relate spectral properties of self-adjoint operators in II1 factors to their images under a conditional expectation onto a maximal abelian subalgebra.
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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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 prove an extension of the latter result for positive trace-class operators on ...
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