Multiplication Operators on the Bloch Space of Infinite Dimensional Bounded Symmetric Domains

摘要

Let B-V be a bounded symmetric domain realized as the unit open ball of a JB*-triple V. Suppose that psi epsilon H(B-V), we will give the necessary and sufficient conditions for the boundedness of multiplicaition operator M-psi on the Bloch space B(B-V). We also give the sufficient conditions such that M-psi is power bounded or is uniformly mean ergodic. Finally, we will prove that M-psi is bounded from below if and only if lim inf(parallel to)(z parallel to -> 1) vertical bar psi(z)vertical bar > 0.