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.


47B38 Linear operators on function spaces (general)
47B33 Linear composition operators
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