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

Extracta Mathematicae (2006)

• Volume: 21, Issue: 1, page 41-50
• ISSN: 0213-8743

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## Abstract

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In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f ∈ H(σ(T)). We also provide several conditions that force an operator with the SVEP to obey a-Weyl's theorem. The author would like to precise that this paper constitute a part of his thesis [16].

## How to cite

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Oudghiri, Mourad. "a-Weyl's theorem and the single valued extension property.." Extracta Mathematicae 21.1 (2006): 41-50. <http://eudml.org/doc/41849>.

@article{Oudghiri2006,
abstract = {In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f ∈ H(σ(T)). We also provide several conditions that force an operator with the SVEP to obey a-Weyl's theorem. The author would like to precise that this paper constitute a part of his thesis [16].},
journal = {Extracta Mathematicae},
keywords = {Operadores lineales; Operadores de Fredholm; Teoría de perturbación; Teorema de Weyl; -Weyl’s theorem; -Browder’s theorem; Weyl's theorem; functional calculus},
language = {eng},
number = {1},
pages = {41-50},
title = {a-Weyl's theorem and the single valued extension property.},
url = {http://eudml.org/doc/41849},
volume = {21},
year = {2006},
}

TY - JOUR
TI - a-Weyl's theorem and the single valued extension property.
JO - Extracta Mathematicae
PY - 2006
VL - 21
IS - 1
SP - 41
EP - 50
AB - In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f ∈ H(σ(T)). We also provide several conditions that force an operator with the SVEP to obey a-Weyl's theorem. The author would like to precise that this paper constitute a part of his thesis [16].
LA - eng
KW - Operadores lineales; Operadores de Fredholm; Teoría de perturbación; Teorema de Weyl; -Weyl’s theorem; -Browder’s theorem; Weyl's theorem; functional calculus
UR - http://eudml.org/doc/41849
ER -

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