Property (\(aw\)) and Weyl's theorem
type: Item
instance of: scholarly article
title: Property (\(aw\)) and Weyl's theorem
zbMATH Open document ID: 1311.47006
author: Il Ju An
author: Young Min Han
published in: Mediterranean Journal of Mathematics
publication date: 2013-08-16T00:00:00Z
review text: In this paper, the authors study the property (\(aw\)), a variant of Weyl's theorem introduced by \textit{M. Berkani} and \textit{H. Zariouh} [Mat. Vesn. 62, No. 2, 145--154 (2010; Zbl 1258.47020)], by means of the localized single valued extension property (SVEP). For a bounded linear operator defined on a Banach space, the authors establish several sufficient and necessary conditions under which property (\(aw\)) holds. The authors also relate this property with Weyl's theorem, \(a\)-Weyl's theorem and property (\(w\)). Finally, the authors show that, if \(T\) is \(a\)-polaroid and either \(T\) or \(T^*\) has the SVEP, then \(f(T)\) satisfies property (\(aw\)) for each \(f \in H_1(\sigma(T)).\)
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 6199105
zbMATH Keywords: property (\(aw\))
zbMATH Keywords: Weyl's theorem
zbMATH Keywords: single-valued extension property (SVEP)
zbMATH Keywords: \(a\)-polaroid operator
reviewed by: Yufeng Lu
MaRDI profile type: Publication
full work available at URL: s00009-013-0251-7
OpenAlex ID: W2076984887
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DOI: 10.1007/S00009-013-0251-7
description: scientific article; zbMATH DE number 6199105