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

Tatsuhiro Honda


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.

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DOI: http://dx.doi.org/10.24193/subbmath.2022.2.08


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