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Differences of composition operators on the Bloch space in the polydisc. (English) Zbl 1166.47032

Summary: Let \(\varphi\) and \(\psi\) be holomorphic self-maps of the unit polydisc \(U^n\) in the \(n\)-dimensional complex space, and denote by \(C_\varphi\) and \(C_\psi\) the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators \(C_\varphi-C_\psi\) from Bloch space to bounded holomorphic function space in the unit polydisc. The compactness of the difference is also characterized.

MSC:

47B38 Linear operators on function spaces (general)
47B33 Linear composition operators
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[1] DOI: 10.1016/j.jmaa.2005.04.080 · Zbl 1087.47029
[2] DOI: 10.1007/s00020-002-1203-y · Zbl 1065.47027
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