Geodesic
A note on the $a$-Browder’s and $a$-Weyl’s theorems
Mathematica Bohemica, Tome 133 (2008) no. 2, pp. 157-166

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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.
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.
DOI : 10.21136/MB.2008.134059
Classification : 47A10, 47A11, 47A53
Keywords: B-Fredholm operator; Weyl’s theorem; Browder’s thoerem; operator of Kato type; single-valued extension property 
Amouch, M.; Zguitti, H. A note on the $a$-Browder’s and $a$-Weyl’s theorems. Mathematica Bohemica, Tome 133 (2008) no. 2, pp. 157-166. doi: 10.21136/MB.2008.134059
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