Classes of operators satisfying a-Weyl's theorem

Pietro Aiena

Studia Mathematica (2005)

  • Volume: 169, Issue: 2, page 105-122
  • ISSN: 0039-3223

Abstract

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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 k e r ( λ I - 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.

How to cite

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Pietro Aiena. "Classes of operators satisfying a-Weyl's theorem." Studia Mathematica 169.2 (2005): 105-122. <http://eudml.org/doc/284546>.

@article{PietroAiena2005,
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 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.},
author = {Pietro Aiena},
journal = {Studia Mathematica},
keywords = {single-valued extension property; Fredholm theory; Weyl's theorems; algebraically paranormal operators},
language = {eng},
number = {2},
pages = {105-122},
title = {Classes of operators satisfying a-Weyl's theorem},
url = {http://eudml.org/doc/284546},
volume = {169},
year = {2005},
}

TY - JOUR
AU - Pietro Aiena
TI - Classes of operators satisfying a-Weyl's theorem
JO - Studia Mathematica
PY - 2005
VL - 169
IS - 2
SP - 105
EP - 122
AB - 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.
LA - eng
KW - single-valued extension property; Fredholm theory; Weyl's theorems; algebraically paranormal operators
UR - http://eudml.org/doc/284546
ER -

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