tailieunhanh - Báo cáo hóa học: "The compactness of the sum of weighted composition operators on the ball algebra"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: The compactness of the sum of weighted composition operators on the ball algebra | Tong and Zhou Journal of Inequalities and Applications 2011 2011 45 http content 2011 1 45 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access The compactness of the sum of weighted composition operators on the ball algebra Ce-Zhong Tong and Ze-Hua Zhou Correspondence zehuazhou2003@ Department of Mathematics Tianjin University Tianjin 300072 People s Republic of China Springer Abstract In this paper we investigate the compactness of the sum of weighted composition operators on the unit ball algebra and give the characterization of compact differences of two weighted composition operators on the ball algebra. The connectness of the topological space consisting of non-zero weighted composition operators on the unit ball algebra is also studied. 2000 Mathematics Subject Classification. Primary 47B33 Secondary 47B38 46E15 32A36. Keywords Weighted composition operator Ball algebra Sum Difference Inequality 1. Introduction Let H BN be the class of all holomorphic functions on BN and S BN the collection of all holomorphic self mappings of BN where BN is the unit ball in the N-dimensional complex space CN. The closure of BN will be written as BN. Denote by A A BN the unit ball algebra of all continuous functions on Bn that are holomorphic on BN. Then A is the Banach algebra with the supremum norm II f TO sup f z z e Bn . And let H H BN be the set of all bounded holomorphic functions on BN. We denote by B A B H resp. the unit ball of A H BN resp. . For u j e A with j e S BN recall that the composition operator Cj induced by j is defined by Cf z f v z the multiplication operator induced by u is defined by Muf z u z f z and the weighted composition operator uCp induced by j and u is defined by uCN z u z f ự z for z e Bn and f e H BN . If let u 1 then uCj Cj if let j id then uCj Mu. It is clear that these operators are linear and uCj is bounded on A. For some results in this topic see for