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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on uniform operators


Author: Hsiao Lan Wang
Journal: Proc. Amer. Math. Soc. 97 (1986), 643-646
MSC: Primary 47B35; Secondary 47A15, 47D25
DOI: https://doi.org/10.1090/S0002-9939-1986-0845981-X
MathSciNet review: 845981
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Abstract: An operator is uniform if its restriction to any infinite-dimensional invariant subspace is unitarily equivalent to itself. We show that a uniform operator having a proper infinite-dimensional invariant subspace resembles an analytic Toeplitz operator in the way that the weakly closed algebra generated by it and the identity operator is isomorphic to a subalgebra of the Calkin algebra; furthermore, this algebra contains no nonscalar operator which is quasi-similar to a normal operator.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0845981-X
Keywords: Uniform operator, Calkin algebra, invariant subspace, normal operator, quasi-similarity, Toeplitz operator
Article copyright: © Copyright 1986 American Mathematical Society