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Title: Single valued extension property and generalized Weyl’s theorem (English)
Author: Berkani, M.
Author: Castro, N.
Author: Djordjević, S. V.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 131
Issue: 1
Year: 2006
Pages: 29-38
Summary lang: English
Category: math
Summary: Let $T$ be an operator acting on a Banach space $X$, let $\sigma (T)$ and $ \sigma _{BW}(T) $ be respectively the spectrum and the B-Weyl spectrum of $T$. We say that $T$ satisfies the generalized Weyl’s theorem if $ \sigma _{BW}(T)= \sigma (T) \setminus E(T)$, where $E(T)$ is the set of all isolated eigenvalues of $T$. The first goal of this paper is to show that if $T$ is an operator of topological uniform descent and $0$ is an accumulation point of the point spectrum of $T,$ then $T$ does not have the single valued extension property at $0$, extending an earlier result of J. K. Finch and a recent result of Aiena and Monsalve. Our second goal is to give necessary and sufficient conditions under which an operator having the single valued extension property satisfies the generalized Weyl’s theorem. (English)
Keyword: single valued extension property
Keyword: B-Weyl spectrum
Keyword: generalized Weyl’s theorem
MSC: 47A10
MSC: 47A53
MSC: 47A55
idZBL: Zbl 1114.47015
idMR: MR2211001
Date available: 2009-09-24T22:23:51Z
Last updated: 2012-06-18
Stable URL:
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