Weyl type theorems for operators satisfying the single-valued extension property. (English) Zbl 1117.47007

Amouch, Mohamed

J. Math. Anal. Appl. 326, No. 2, 1476-1484 (2007).

Let \(T\) be a bounded linear operator acting on a Banach space \(X\) such that \(T\) or its adjoint \(T^*\) has the single-valued extension property. It is proved that the spectral mapping theorem holds for the B-Weyl spectrum. It is also shown that the generalized Browder’s theorem holds for \(f(T)\) for every analytic function \(f\) defined on an open neighborhood \(U\) of \(\sigma(T)\). Moreover, necessary and sufficient conditions for such \(T\) to satisfy the generalized Weyl’s theorem are observed. Some applications are also given.

Reviewer: Vladislav Skopin (Lipetsk)

MSC:

47A53	(Semi-) Fredholm operators; index theories
47A10	Spectrum, resolvent

Keywords:

B-Fredholm operator; B-Weyl spectrum; generalized Weyl’s theorem; single-valued extension property (SVEP)

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