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On decomposability of compact perturbations of operators


Author: M. Radjabalipour
Journal: Proc. Amer. Math. Soc. 53 (1975), 159-164
MSC: Primary 47B40; Secondary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1975-0407650-2
MathSciNet review: 0407650
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Abstract: Let $ A$ be a Hilbert-space operator satisfying the growth condition $ \vert\vert{(z - A)^{ - 1}}\vert\vert \leqslant \exp \{ K{[\operatorname{dist} (z,\;J)]^{ - S}}\} ,\;z \notin J$, where $ J$ is a $ {C^2}$ Jordan curve, and $ K > 0,\;s\epsilon (0,\;1)$ are two constants. Let $ T = A + B$ for some $ B\epsilon {C_p},\;1 \leqslant p < \infty $. It is shown that $ T$ is strongly decomposable if and only if $ \sigma (T)$ does not fill the ``interior'' of $ J$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0407650-2
Keywords: Hilbert space, bounded operator, invariant subspace, growth condition, compact operator
Article copyright: © Copyright 1975 American Mathematical Society

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