Property (\(aw\)) and Weyl’s theorem. (English) Zbl 1311.47006
In this paper, the authors study the property (\(aw\)), a variant of Weyl’s theorem introduced by M. Berkani and 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 \(f \in H_1(\sigma(T)).\)
Reviewer: Yufeng Lu (Dalian)
MSC:
| 47A10 | Spectrum, resolvent |
| 47A53 | (Semi-) Fredholm operators; index theories |
| 47B20 | Subnormal operators, hyponormal operators, etc. |
Keywords:
property (\(aw\)); Weyl’s theorem; single-valued extension property (SVEP); \(a\)-polaroid operatorCitations:
Zbl 1258.47020References:
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