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.
@article{urn:eudml:doc:41850,
title = {Generalized a-Weyl's theorem and the single-valued extension property.},
journal = {Extracta Mathematicae},
volume = {21},
year = {2006},
pages = {51-65},
zbl = {1123.47005},
mrnumber = {MR2258341},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41850}
}
Amouch, Mohamed. Generalized a-Weyl's theorem and the single-valued extension property.. Extracta Mathematicae, Tome 21 (2006) pp. 51-65. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41850/