Resumen de Generalized a-Weyl's theorem and the single-valued extension property

Mohamed Amouch

• Let T be a bounded linear operator acting on a Banach space X such that T or T* has the SVEP. We prove that the spectral mapping theorem holds for the semi-essential approximate point spectrum ¿SBF-+ (T); and we show that generalized a-Browder's theorem holds for f(T) for every analytic function f defined on an open neighbourhood U of [sigma](T): Moreover, we give a necessary and sufficient condition for such T to obey generalized a-Weyl's theorem. An application is given for an important class of Banach space operators.