Operators of the α-Bloch space on the open unit ball of a JB*-triple

Abstract

Let $\B_X$ be a bounded symmetric domain realized as the open unit ball of
a JB*-triple $X$ which may be infinite dimensional.
In this paper, we characterize the bounded weighted composition operators from the Hardy space $H^{\infty}(\mathbb{B}_X)$
into the $\alpha $-Bloch space $\mathcal{B}^\alpha (\B_X)$ on $\mathbb{B}_X$.
Later, we show the multiplication operator from $H^{\infty}(\mathbb{B}_X)$ into $\mathcal{B}^\alpha (\B_X)$ is bounded.
Also, we give the operator norm of the bounded multiplication operator.