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

Mathematica Bohemica (2008)

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

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topAmouch, 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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