### A note on the $a$-Browder’s and $a$-Weyl’s theorems

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 ${E}^{a}\left(T\right)={\pi}^{a}\left(T\right),$ where ${E}^{a}\left(T\right)$ is the set of all eigenvalues of $T$ which are isolated in the approximate point spectrum and ${\pi}^{a}\left(T\right)$ is the set of all left poles of $T.$ Some applications are also given.