Indecomposable compact perturbations of the bilateral shift

Herrero, Domingo A.

doi:10.1090/S0002-9939-1977-0435922-6

Indecomposable compact perturbations of the bilateral shift
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by Domingo A. Herrero PDF

Proc. Amer. Math. Soc. 62 (1977), 254-258 Request permission

Abstract:

Recent results of M. Radjabalipour and H. Radjavi assert that the sum of a normal operator N with spectrum on a smooth Jordan curve and a compact operator K in the Macaev ideal ${\mathfrak {S}_\omega }$ is decomposable provided the spectrum of $N + K$ does not fill the interior of the curve. Examples are given to show that this result cannot be essentially improved by taking K in a larger ideal.

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On invariant subspaces of compact perturbations of operators