Compact Differences Of Weighted Composition Operators On H~∞(B_N)

In this paper, we characterize the compactness of differences of two weighted com-position operators on the space of bounded analytic functions on the open unit ball in the uniform operator topology. We give a sufficient condition when two weighted compo-sition operators lie in the same component of the space of nonzero weighted composition operators on H∞(BN), which is denoted by Cw(H∞(BN)).The article is divided into four chapters.In the first chapter, we introduce the development as well as important results and conjectures of compact difference and topological structure of (weighted) composition operator on various of spaces of analytic functions;In the second chapter, we outline some preliminary definitions and lemmas;In the third chapter, we give a proof of the main theorem in detail which charac-terize compact difference for two weighted composition operators acting on H∞(BN);In the last chapter, we give a sufficient condition when two weighted composition operators lie in the same component of the space of nonzero weighted composition operators on H∞(BN).