A Note on the Browder's and Weyl's Theorem

Let T be a Banach space operator, E(T) be the set of all isolated eigenvalues of T and pi(T) be the set of all poles of T. In this work, we show that Browder's theorem for T is equivalent to the localized single-valued extension property at all complex numbers lambda in the complement of the Weyl spectrum of T, and we give some characterization of Weyl's theorem for operator satisfying E(T) = pi(T). An application is also given.