A note on the a -Browder’s and a -Weyl’s theorems

M. Amouch; H. Zguitti

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 2, page 157-166
  • ISSN: 0862-7959

Abstract

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Let T be a Banach space operator. In this paper we characterize a -Browder’s theorem for T by the localized single valued extension property. Also, we characterize a -Weyl’s theorem under the condition E a ( T ) = π a ( T ) , where E a ( T ) is the set of all eigenvalues of T which are isolated in the approximate point spectrum and π a ( T ) is the set of all left poles of T . Some applications are also given.

How to cite

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Amouch, M., and Zguitti, H.. "A note on the $a$-Browder’s and $a$-Weyl’s theorems." Mathematica Bohemica 133.2 (2008): 157-166. <http://eudml.org/doc/250520>.

@article{Amouch2008,
abstract = {Let $T$ be a Banach space operator. In this paper we characterize $a$-Browder’s theorem for $T$ by the localized single valued extension property. Also, we characterize $a$-Weyl’s theorem under the condition $E^a(T)=\pi ^a(T),$ where $E^a(T)$ is the set of all eigenvalues of $T$ which are isolated in the approximate point spectrum and $\pi ^a(T)$ is the set of all left poles of $T.$ Some applications are also given.},
author = {Amouch, M., Zguitti, H.},
journal = {Mathematica Bohemica},
keywords = {B-Fredholm operator; Weyl’s theorem; Browder’s thoerem; operator of Kato type; single-valued extension property; B-Fredholm operator; Weyl's theorem; operator of Kato type; single-valued extension property (SVEP)},
language = {eng},
number = {2},
pages = {157-166},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the $a$-Browder’s and $a$-Weyl’s theorems},
url = {http://eudml.org/doc/250520},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Amouch, M.
AU - Zguitti, H.
TI - A note on the $a$-Browder’s and $a$-Weyl’s theorems
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 2
SP - 157
EP - 166
AB - Let $T$ be a Banach space operator. In this paper we characterize $a$-Browder’s theorem for $T$ by the localized single valued extension property. Also, we characterize $a$-Weyl’s theorem under the condition $E^a(T)=\pi ^a(T),$ where $E^a(T)$ is the set of all eigenvalues of $T$ which are isolated in the approximate point spectrum and $\pi ^a(T)$ is the set of all left poles of $T.$ Some applications are also given.
LA - eng
KW - B-Fredholm operator; Weyl’s theorem; Browder’s thoerem; operator of Kato type; single-valued extension property; B-Fredholm operator; Weyl's theorem; operator of Kato type; single-valued extension property (SVEP)
UR - http://eudml.org/doc/250520
ER -

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