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

Pietro Aiena; Carlos Carpintero

Extracta Mathematicae (2005)

- Volume: 20, Issue: 1, page 25-41
- ISSN: 0213-8743

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topAiena, Pietro, and Carpintero, Carlos. "Weyl's theorem, a-Weyl's theorem and single-valued extension property.." Extracta Mathematicae 20.1 (2005): 25-41. <http://eudml.org/doc/38776>.

@article{Aiena2005,

abstract = {In this paper we investigate the relation of Weyl's theorem, of a-Weyl's theorem and the single valued extension property. In particular, we establish necessary and sufficient conditions for a Banch space operator T to satisfy Weyl's theorem or a-Weyl's theorem, in the case in which T, or its dual T*, has the single valued extension property. These results improve similar results obtained by Curto and Han, Djordjevic S. V., Duggal B. P., and Y. M. Han. The theory is exemplified in the case of multipliers of commutative semi-simple Banach algebras, in particular convolution operators on the group algebra L1(G), weighted shift operators on lp(N), with 1 ≤ p < ∞, as well as other classes of operators.},

author = {Aiena, Pietro, Carpintero, Carlos},

journal = {Extracta Mathematicae},

keywords = {spectrum; Weyl spectrum; Weyl's theorem; single-valued extension property},

language = {eng},

number = {1},

pages = {25-41},

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

url = {http://eudml.org/doc/38776},

volume = {20},

year = {2005},

}

TY - JOUR

AU - Aiena, Pietro

AU - Carpintero, Carlos

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

JO - Extracta Mathematicae

PY - 2005

VL - 20

IS - 1

SP - 25

EP - 41

AB - In this paper we investigate the relation of Weyl's theorem, of a-Weyl's theorem and the single valued extension property. In particular, we establish necessary and sufficient conditions for a Banch space operator T to satisfy Weyl's theorem or a-Weyl's theorem, in the case in which T, or its dual T*, has the single valued extension property. These results improve similar results obtained by Curto and Han, Djordjevic S. V., Duggal B. P., and Y. M. Han. The theory is exemplified in the case of multipliers of commutative semi-simple Banach algebras, in particular convolution operators on the group algebra L1(G), weighted shift operators on lp(N), with 1 ≤ p < ∞, as well as other classes of operators.

LA - eng

KW - spectrum; Weyl spectrum; Weyl's theorem; single-valued extension property

UR - http://eudml.org/doc/38776

ER -