Single valued extension property and generalized Weyl’s theorem

Berkani, M., Castro, N., and Djordjević, S. V.. "Single valued extension property and generalized Weyl’s theorem." Mathematica Bohemica 131.1 (2006): 29-38. <http://eudml.org/doc/249899>.

@article{Berkani2006,
abstract = {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.},
author = {Berkani, M., Castro, N., Djordjević, S. V.},
journal = {Mathematica Bohemica},
keywords = {single valued extension property; B-Weyl spectrum; generalized Weyl’s theorem; B-Weyl spectrum; SVEP; generalised Weyl theorem},
language = {eng},
number = {1},
pages = {29-38},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Single valued extension property and generalized Weyl’s theorem},
url = {http://eudml.org/doc/249899},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Berkani, M.
AU - Castro, N.
AU - Djordjević, S. V.
TI - Single valued extension property and generalized Weyl’s theorem
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 1
SP - 29
EP - 38
AB - 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.
LA - eng
KW - single valued extension property; B-Weyl spectrum; generalized Weyl’s theorem; B-Weyl spectrum; SVEP; generalised Weyl theorem
UR - http://eudml.org/doc/249899
ER -