Abstract and Applied Analysis
Volume 2008 (2008), Article ID 983132, 10 pages
Research Article

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

Received 30 May 2008; Revised 27 August 2008; Accepted 14 November 2008

Academic Editor: Stevo Stević

Copyright © 2008 Zhong-Shan Fang and Ze-Hua Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.