On the equivalence of Browder's and generalized Browder's theorem

In this note we answer two question posed by Berkani and Koliha [Acta Sci. Math. 69 (2003), 359-376]. We show that generalized Browder's (resp. generalized a-Browder's) theorem holds for a Banach space operator if and only if Browder's (resp. a-Browder's) theorem does. We also give condition under which generalized Weyl's (resp. generalized a-Weyl's) theorem is equivalent to Weyl's (resp. a-Weyl's) theorem.