Bloch Space of a Bounded Symmetric Domain and Composition Operators

摘要

We generalize a number of finite dimensional results on Bloch functions to infinite dimensional bounded symmetric domains. In particular, we characterize the Bloch space as well as the little Bloch space of a Hilbert ball, and give one sufficient and several necessary conditions for a composition operator on a Bloch space to be an isometry. We also answer some open questions of Allen and Colonna concerning Bloch functions and composition operators.