Property (\(aw\)) and Weyl's theorem
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 \(f \in H_1(\sigma(T)).\)
scientific article; zbMATH DE number 6199105