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Keywords:
B-Fredholm operator; Weyl’s theorem; Browder’s thoerem; operator of Kato type; single-valued extension property
B-Fredholm operator; Weyl’s theorem; Browder’s thoerem; operator of Kato type; single-valued extension property
Summary:
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.
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