In this article Weyl’s theorem and a-Weyl’s theorem on Banach spaces are related to an important property which has a leading role in local spectral theory: the single-valued extension theory. We show that if T has SVEP then Weyl’s theorem and a-Weyl’s theorem for T* are equivalent, and analogously, if T* has SVEP then Weyl’s theorem and a-Weyl’s theorem for T are equivalent. From this result we deduce that a-Weyl’s theorem holds for classes of operators for which the quasi-nilpotent part H₀(λI - T) is equal to for some p ∈ ℕ and every λ ∈ ℂ, and for algebraically paranormal operators on Hilbert spaces. We also improve recent results established by Curto and Han, Han and Lee, and Oudghiri.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-2-1,
author = {Pietro Aiena},
title = {Classes of operators satisfying a-Weyl's theorem},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {105-122},
zbl = {1071.47001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-2-1}
}
Pietro Aiena. Classes of operators satisfying a-Weyl's theorem. Studia Mathematica, Tome 166 (2005) pp. 105-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-2-1/