On the isometric composition operators on the Bloch space in C^n

Details On the isometric composition operators on the Bloch space in C^n On the isometric composition operators on the Bloch space in C^n

2008-09-19

arxiv.org/abs/0809.3438v1

Mathematics

Functional Analysis

Scientific paper

Let phi be a holomorphic self-map of a bounded homogeneous domain D in C^n. In this work, we show that the composition operator C_phi is bounded on the Bloch space B of the domain and provide estimates on its operator norm. We also give a sufficient condition for phi to induce an isometry on B. This condition allows us to construct non-trivial examples of isometric composition operators in the case when D has the unit disk as a factor. We then obtain some necessary conditions for C_phi to be an isometry on B when D is a Cartan classical domain. Finally, we give the complete description of the spectrum of the isometric composition operators in the case of the unit disk and for a wide class of symbols on the polydisk.

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