On decomposability of compact perturbations of operators
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- by M. Radjabalipour PDF
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Abstract:
Let $A$ be a Hilbert-space operator satisfying the growth condition $||{(z - A)^{ - 1}}|| \leqslant \exp \{ K{[\operatorname {dist} (z,\;J)]^{ - S}}\} ,\;z \notin J$, 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 $J$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- 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