Classes of operators satisfying a-Weyl's theorem

• Autorzy: Pietro Aiena
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 47A55: Perturbation theory
• 47A11: Local spectral properties
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 169
• Numer: 2
• Strony: 105-122

Daty

wydano

2005

Twórcy

autor

Pietro Aiena

• Dipartimento di Metodi e Modelli Matematici, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy

Identyfikatory

DOI

10.4064/sm169-2-1