Extended Weyl type theorems

Berkani, M., and Zariouh, H.. "Extended Weyl type theorems." Mathematica Bohemica 134.4 (2009): 369-378. <http://eudml.org/doc/38099>.

@article{Berkani2009,
abstract = {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. 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 $T.$},
author = {Berkani, M., Zariouh, H.},
journal = {Mathematica Bohemica},
keywords = {B-Fredholm operator; Browder’s theorem; generalized Browder’s theorem; property $(\{\rm b\})$; property $(\{\rm gb\})$; B-Fredholm operator; Browder's theorem; generalized Browder's theorem; property (b); property (gb)},
language = {eng},
number = {4},
pages = {369-378},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extended Weyl type theorems},
url = {http://eudml.org/doc/38099},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Berkani, M.
AU - Zariouh, H.
TI - Extended Weyl type theorems
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 4
SP - 369
EP - 378
AB - 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. 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 $T.$
LA - eng
KW - B-Fredholm operator; Browder’s theorem; generalized Browder’s theorem; property $({\rm b})$; property $({\rm gb})$; B-Fredholm operator; Browder's theorem; generalized Browder's theorem; property (b); property (gb)
UR - http://eudml.org/doc/38099
ER -