On the property $(Z_{E_a})$
On the property $(Z_{E_a})$
The paper introduces the notion of properties $(Z_{��_a})$ and $(Z_{E_a})$ as variants of Weyl's theorem and Browder's theorem for bounded linear operators acting on infinite dimensional Banach spaces. A characterization of these properties in terms of localized single valued extension property is given, and the perturbation by commuting Riesz operators is also studied. Classes of operators are considered as illustrating examples.
10 pages
Local spectral properties of linear operators, Perturbation theory of linear operators, Weyl's theorem, SVEP, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, (Semi-) Fredholm operators; index theories, Spectrum, resolvent, property \((Z_{E_{a}})\), 47A53, 47A55, 47A10, 47A11, Riesz operator
Local spectral properties of linear operators, Perturbation theory of linear operators, Weyl's theorem, SVEP, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, (Semi-) Fredholm operators; index theories, Spectrum, resolvent, property \((Z_{E_{a}})\), 47A53, 47A55, 47A10, 47A11, Riesz operator
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