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

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