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MATHEMATICA BOHEMICA, Vol. 133, No. 2, pp. 157-166 (2008)
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A note on the $a$-Browder's and $a$-Weyl's theorems

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M. Amouch, H. Zguitti

* 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 (MSC2000):** 47A53, 47A10, 47A11

**Full text of the article:**

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