Topological Uniform Descent and Judgement of A-Weyl's Theorem

In this paper, a-Browder's theorem and a-Weyl's theorem for bounded linear operators are studied by means of the property of the topological uniform descent. The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding a-Browder's theorem and a-Weyl's theorem are established. As a consequence of the main result, the new judgements of a-Browder's theorem and a-Weyl's theorem for operator function are discussed.