Some unsolved problems of unknown depth about operators on Hilbert space

DOI10.1017/S0308210500019491zbMath0346.47001MaRDI QIDQ4115679

Paul R. Halmos

Publication date: 1976

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Invariant subspaces of linear operators (47A15) Dilations, extensions, compressions of linear operators (47A20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Canonical models for contractions and nonselfadjoint linear operators (47A45) Canonical forms, reductions, classification (15A21)

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Cites Work

• Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos
• Invariant subspaces and unstarred operator algebras
• Weyl's theorem for nonnormal operators
• A density theorem for operator algebras
• Products of shifts
• Invariant subspaces of completely continuous operators
• The Spectra of Toeplitz's Matrices
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