Abstract: We considered A-Browder’s theorem and A-Weyl’s theorem of Weyl theorem. By using the topological uniform descent method, we obtained a new equivalent condition and decision method for arbitrary C∈B(H), operator M_C satisfying A-Browder’s theorem and the A-Weyl’s theorem under small compact perturbations.

Key words: A-Browder’s theorem, A-Weyl’s theorem, compact perturbation