Differences of composition operators on the space of bounded analytic functions in the polydisc. (English) Zbl 1160.32009

Fang, Zhong-Shan; Zhou, Ze-Hua

Abstr. Appl. Anal. 2008, Article ID 983132, 10 p. (2008).

Summary: This paper gives some estimates of the essential norm for the difference of composition operators induced by \(\varphi \) and \(\psi \) acting on the space \(H^{\infty }(D^{n})\) of bounded analytic functions on the unit polydisc \(D^{n}\), where \(\varphi \) and \(\psi \) are holomorphic self-maps of \(D^{n}\). As a consequence, one obtains conditions in terms of the Carathéodory distance on \(D^{n}\) that characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators on \(H^{\infty }(D^{n})\) is compact.

MSC:

32A37	Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
47B33	Linear composition operators

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