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Differences of composition operators between weighted Banach spaces of holomorphic functions on the unit polydisk. (English) Zbl 1154.47018

By introducing an auxiliary associated weight, the author gives an estimate in terms of pseudohyperbolic distance for the essential norm of the difference of composition operators between given weighted Banach spaces \(H_v^\infty\) or \(H_v^0\) of holomorphic functions on the unit polydisk. This result can lead to conditions for the differences to be compact.

MSC:

47B33 Linear composition operators
47B38 Linear operators on function spaces (general)
32A10 Holomorphic functions of several complex variables
47B39 Linear difference operators
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