Diference Of Weighted Composition Operators From α-bloch Space To H∞on The Unit Ball

The boundness and compactness of the diferences of weighted composition opera-tors between diferent analytic function spaces is a very important part of operator theory.According to the choose of α, in this paper, we study the boundness and compactness ofdiferences of weighted composition operators acting from the α Bloch space Bαto thespace H∞of bounded analytic functions on the open unit ball of Cn. Moreover, we estimatethe norm and essential norm of diferences of composition operators from B to H∞.The paper mainly split into the following five chapters.The first chapter is the background of the branch of operator theory and the recentwork of the problem that we are interested in. Thus, lead to the study of the paper.The second chapter of the paper, some important concepts and lemmas which arerelated to the article are given. They are the foundations and tools of the later work, and wewill use them without proof.In the third chapter, considering α>1, we discusses the necessary and sufcient con-ditions of boundness and compactness of the diferences of weighted composition operatoracting from Bαto H∞on the unit ball.In the fourth chapter, we study the necessary and sufcient conditions of boundnessand compactness of the diferences of weighted composition operator acting B to H∞onthe unit ball in the view of sequence. Moreover, we estimate the norm and essential normof diference of composition operators from B to H∞.In last part, we characterizes the boundedness of the diferences of weighted compo-sition operators acting from Bαto H∞when0<α <1on the unit ball. But portray thecompactness is difcult, we can only give a sufcient condition.