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

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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.

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Authors and Affiliations

  1. Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai, 2-Chome, Higashi-ku, Fukuoka, 813-8503, Japan

    Hidetaka Hamada

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  1. Hidetaka Hamada
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Correspondence to Hidetaka Hamada.

Additional information

Communicated by Simeon Reich.

H. Hamada was partially supported by JSPS KAKENHI Grant Number JP16K05217.

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Hamada, H. Weighted Composition Operators from \(H^{\infty }\) to the Bloch Space of Infinite Dimensional Bounded Symmetric Domains. Complex Anal. Oper. Theory 12, 207–216 (2018). https://doi.org/10.1007/s11785-016-0624-6

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  • DOI: https://doi.org/10.1007/s11785-016-0624-6

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