Essentially subnormal operators and 𝐾-spectral sets

Lange, Ridgley

doi:10.1090/S0002-9939-1983-0699412-0

Essentially subnormal operators and $K$-spectral sets
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Proc. Amer. Math. Soc. 88 (1983), 449-453 Request permission

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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An extension of Scott Brown’s subspace theorem:

-spectral sets

3