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Title: Extended Weyl type theorems (English)
Author: Berkani, M.
Author: Zariouh, H.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 134
Issue: 4
Year: 2009
Pages: 369-378
Summary lang: English
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Category: math
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Summary: An operator $T$ acting on a Banach space $X$ possesses property $({\rm gw})$ if $\sigma _a(T)\setminus \sigma _{{\rm SBF}_+^-}(T)= E(T), $ where $\sigma _a(T)$ is the approximate point spectrum of $T$, $\sigma _{{\rm SBF} _+^-}(T)$ is the essential semi-B-Fredholm spectrum of $T$ and $E(T)$ is the set of all isolated eigenvalues of $T.$ In this paper we introduce and study two new properties $({\rm b})$ and $({\rm gb})$ in connection with Weyl type theorems, which are analogous respectively to Browder's theorem and generalized Browder's theorem. \endgraf Among other, we prove that if $T$ is a bounded linear operator acting on a Banach space $X$, then property $({\rm gw})$ holds for $T$ if and only if property $({\rm gb})$ holds for $T$ and $E(T)=\Pi (T),$ where $\Pi (T)$ is the set of all poles of the resolvent of $T.$ (English)
Keyword: B-Fredholm operator
Keyword: Browder's theorem
Keyword: generalized Browder's theorem
Keyword: property $({\rm b})$
Keyword: property $({\rm gb})$
MSC: 47A10
MSC: 47A11
MSC: 47A53
idZBL: Zbl 1211.47011
idMR: MR2597232
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Date available: 2010-07-20T18:10:24Z
Last updated: 2013-09-20
Stable URL: http://hdl.handle.net/10338.dmlcz/140669
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