Chaotic composition operators on the classical holomorphic spaces

Abstract

We call the composition operator induced by a biholomorphic automorphism of the unit disc U a Möbius composition operator. Here, if φ has a fixed point in U, then we call φ elliptic. In this paper, we give an elementary proof to the fact that a Möbius composition operator is chaotic on the Hardy space H^p and on the Bergman space B^p for every p∈ (0,+∞) if and only if the corresponding φ is non-elliptic. This result is a generalization of Hosokawa's results.

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