Proceedings of the American Mathematical Society

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

 

 

Indecomposable compact perturbations of the bilateral shift


Author: Domingo A. Herrero
Journal: Proc. Amer. Math. Soc. 62 (1977), 254-258
MSC: Primary 47B37; Secondary 47A65
MathSciNet review: 0435922
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0435922-6
Keywords: Bilateral weighted shifts, decomposable operators, Macaev ideal of compact operators
Article copyright: © Copyright 1977 American Mathematical Society