Abstract and Applied Analysis
Volume 2008 (2008), Article ID 983132, 10 pages
doi:10.1155/2008/983132
Differences of composition operators on the space of bounded analytic functions in the polydisc
Zhong-Shan Fang1
and Ze-Hua Zhou2
1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Mathematics, Tianjin University, Tianjin 300072, China
Abstract
This paper gives some estimates of the essential norm for the difference of composition operators induced by φ and ψ acting on the space, H∞(Dn), of bounded analytic functions on the unit polydisc Dn, where φ and ψ are holomorphic self-maps of Dn. As a consequence, one obtains conditions in terms of the Carathéodory distance on Dn that characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators on H∞(Dn) is compact.