M. Amouch, Department of Mathematics, Faculty of Science of Semlalia, B.O. 2390 Marrakesh, Morocco, e-mail: m.amouch@ucam.ac.ma; H. Zguitti, Department of Mathematics, Faculty of Science of Rabat, B.O. 1014 Rabat, Morocco, e-mail: zguitti@hotmail.com
Abstract: Let $T$ be a Banach space operator. In this paper we characterize $a$-Browder's theorem for $T$ by the localized single valued extension property. Also, we characterize $a$-Weyl's theorem under the condition $E^a(T)=\pi^a(T),$ where $E^a(T)$ is the set of all eigenvalues of $T$ which are isolated in the approximate point spectrum and $\pi^a(T)$ is the set of all left poles of $T.$ Some applications are also given.
Keywords: B-Fredholm operator, Weyl's theorem, Browder's thoerem, operator of Kato type, single-valued extension property
Classification (MSC 2000): 47A53, 47A10, 47A11
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