Differences of Composition Operators on the Space of Bounded Analytic Functions in the Polydisc

Zhong-Shan Fang; Ze-Hua Zhou
January 2008
Abstract & Applied Analysis;2008, p1
Academic Journal
This paper gives some estimates of the essential norm for the difference of composition operators induced by φ and φ acting on the space, H∞(Dn), of bounded analytic functions on the unit polydisc DE;n, where φ and φ 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.


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