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Some unsolved problems of unknown depth about operators on Hilbert space

Published online by Cambridge University Press:  14 February 2012

P. R. Halmos
P. R. Halmos
Affiliation:
Department of Mathematics, University of California (Santa Barbara)
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Synopsis

The paper presents a list of unsolved problems about operators on Hilbert space, accompanied by just enough definitions and general discussion to set the problems in a reasonable context. The subjects are: quasitriangular matrices, the resemblances between normal and Toeplitz operators, dilation theory, the algebra of shifts, some special invariant subspaces, the category (in the sense of Baire) of the set of non-cyclicoperators, non-commutative(i.e. operator) approximation theory, infinitary operators, and the possibility of attacking invariance problems by compactness or convexity arguments.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 1 , 1976 , pp. 67 - 76
Copyright
Copyright © Royal Society of Edinburgh 1976

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