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Essential norm of the difference of composition operators on Bloch space. (English) Zbl 1220.47045

Summary: Let \(\varphi \) and \(\psi \) be holomorphic self-maps of the unit disk, and denote by \(C_{\varphi }\), \(C_{\psi }\) 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 spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.

MSC:

47B38 Linear operators on function spaces (general)
47B33 Linear composition operators
46E15 Banach spaces of continuous, differentiable or analytic functions
30H30 Bloch spaces
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