We study Weyl's and Browder's theorem for an operator T on a Banach space such that T or its adjoint has the single-valued extension property. We establish the spectral mapping theorem for the Weyl spectrum, and we show that Browder's theorem holds for f(T) for every f ∈ 𝓗 (σ(T)). Also, we give necessary and sufficient conditions for such T to obey Weyl's theorem. Weyl's theorem in an important class of Banach space operators is also studied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-1-5,
author = {Mourad Oudghiri},
title = {Weyl's and Browder's theorems for operators satisfying the SVEP},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {85-101},
zbl = {1064.47004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-1-5}
}
Mourad Oudghiri. Weyl's and Browder's theorems for operators satisfying the SVEP. Studia Mathematica, Tome 162 (2004) pp. 85-101. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-1-5/