On generalized a-Browder's theorem

We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H₀(λI - T) as λ belongs to certain sets of ℂ. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators.