# Generalized a-Weyl's theorem and the single-valued extension property.

Extracta Mathematicae (2006)

- Volume: 21, Issue: 1, page 51-65
- ISSN: 0213-8743

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topAmouch, Mohamed. "Generalized a-Weyl's theorem and the single-valued extension property.." Extracta Mathematicae 21.1 (2006): 51-65. <http://eudml.org/doc/41850>.

@article{Amouch2006,

abstract = {Let T be a bounded linear operator acting on a Banach space X such that T or T* has the single-valued extension property (SVEP). We prove that the spectral mapping theorem holds for the semi-essential approximate point spectrum σSBF-+(T); and we show that generalized a-Browder's theorem holds for f(T) for every analytic function f defined on an open neighbourhood U of σ(T): Moreover, we give a necessary and sufficient condition for such T to obey generalized a-Weyl's theorem. An application is given for an important class of Banach space operators.},

author = {Amouch, Mohamed},

journal = {Extracta Mathematicae},

keywords = {Operadores lineales; Operadores de Fredholm; Espectros; Teorema de Weyl; generalised Weyl's theorem; generalised Browder's theorem; generalised -Weyl’s theorem; generalised -Browder’s theorem; semi-essential approximate point spectrum; -Fredholm and semi--Fredholm operators; SVEP},

language = {eng},

number = {1},

pages = {51-65},

title = {Generalized a-Weyl's theorem and the single-valued extension property.},

url = {http://eudml.org/doc/41850},

volume = {21},

year = {2006},

}

TY - JOUR

AU - Amouch, Mohamed

TI - Generalized a-Weyl's theorem and the single-valued extension property.

JO - Extracta Mathematicae

PY - 2006

VL - 21

IS - 1

SP - 51

EP - 65

AB - Let T be a bounded linear operator acting on a Banach space X such that T or T* has the single-valued extension property (SVEP). We prove that the spectral mapping theorem holds for the semi-essential approximate point spectrum σSBF-+(T); and we show that generalized a-Browder's theorem holds for f(T) for every analytic function f defined on an open neighbourhood U of σ(T): Moreover, we give a necessary and sufficient condition for such T to obey generalized a-Weyl's theorem. An application is given for an important class of Banach space operators.

LA - eng

KW - Operadores lineales; Operadores de Fredholm; Espectros; Teorema de Weyl; generalised Weyl's theorem; generalised Browder's theorem; generalised -Weyl’s theorem; generalised -Browder’s theorem; semi-essential approximate point spectrum; -Fredholm and semi--Fredholm operators; SVEP

UR - http://eudml.org/doc/41850

ER -

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