A note on uniform operators

Author:
Hsiao Lan Wang

Journal:
Proc. Amer. Math. Soc. **97** (1986), 643-646

MSC:
Primary 47B35; Secondary 47A15, 47D25

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