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## Studia Mathematica

2005 | 169 | 2 | 105-122
Tytuł artykułu

### Classes of operators satisfying a-Weyl's theorem

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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 $ker(λI - T)^{p}$ 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.
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105-122
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wydano
2005
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• Dipartimento di Metodi e Modelli Matematici, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
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