Classes of operators satisfying a-Weyl's theorem

Pietro Aiena, Pietro Aiena

Risultato della ricerca: Article

43 Citazioni (Scopus)

Abstract

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 H 0(λI-T) is equal to ker (λI -T)p 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.
Lingua originaleEnglish
pagine (da-a)105-122
Numero di pagine18
RivistaStudia Mathematica
Volume169
Stato di pubblicazionePublished - 2005

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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