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.
@article{urn:eudml:doc:38776,
title = {Weyl's theorem, a-Weyl's theorem and single-valued extension property.},
journal = {Extracta Mathematicae},
volume = {20},
year = {2005},
pages = {25-41},
zbl = {1079.47002},
mrnumber = {MR2149122},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38776}
}
Aiena, Pietro; Carpintero, Carlos. Weyl's theorem, a-Weyl's theorem and single-valued extension property.. Extracta Mathematicae, Tome 20 (2005) pp. 25-41. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38776/