Displaying similar documents to “The singular sequence problem”

Diagonals of Self-adjoint Operators with Finite Spectrum

Marcin Bownik, John Jasper (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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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).

A perturbation characterization of compactness of self-adjoint operators

Heydar Radjavi, Ping-Kwan Tam, Kok-Keong Tan (2003)

Studia Mathematica

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A characterization of compactness of a given self-adjoint bounded operator A on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator A, which is necessary and sufficient for the perturbation, is given.

A characterization of the essential spectrum and applications

Aref Jeribi (2002)

Bollettino dell'Unione Matematica Italiana

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In this article the essential spectrum of closed, densely defined linear operators is characterized on a large class of spaces, which possess the Dunford-Pettis property or which isomorphic to one of the spaces L p ⁢ Ω p > 1 . A practical criterion guaranteeing its stability, for perturbed operators, is given. Further we apply the obtained results to investigate the essential spectrum of one-dimensional transport equation with general boundary conditions. Finally, sufficient conditions...