Weighted Composition Operators from $$H^{\infty }$$ H ∞ to the Bloch Space of Infinite Dimensional Bounded Symmetric Domains

Abstract

Let \(\mathbb {B}_X\) be a bounded symmetric domain realized as the open unit ball of a JB*-triple X. In this paper, we characterize the bounded weighted composition operators from the Hardy space \(H^{\infty }(\mathbb {B}_X)\) into the Bloch space on \(\mathbb {B}_X\). We also give estimates on the operator norm. The lower estimate is an improvement of the result known. We show that the bounded multiplication operators from \(H^{\infty }(\mathbb {B}_X)\) into the Bloch space on \(\mathbb {B}_X\) are precisely those whose symbols are bounded. We also determine the operator norm of the bounded multiplication operator. As a corollary, we show that there are no isometric multiplication operators. Finally, we show that there are no isometric composition operators.