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Proceedings of the American Mathematical Society

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Essentially subnormal operators and $ K$-spectral sets

Author: Ridgley Lange
Journal: Proc. Amer. Math. Soc. 88 (1983), 449-453
MSC: Primary 47A15; Secondary 47B20
MathSciNet review: 699412
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Abstract: Let $ T$ be an essentially subnormal operator. We give six conditions which are equivalent to the spectrum of $ T$ being a $ K$-spectral set. From this follow two corollaries which give sufficient conditions for invariant subspaces of essentially subnormal operators. Several examples are given that show that some essentially subnormal operators are not essentially normal nor perturbations of subnormal operators.

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Keywords: Essentially subnormal operators, $ K$-spectral set, invariant subspace
Article copyright: © Copyright 1983 American Mathematical Society