Abstract
Let \(\mathbb {B}_X\) be a bounded symmetric domain realized as the open unit ball \(\mathbb {B}_X\) of a finite dimensional JB*-triple X. In this paper, we continue the work related to α-Bloch mappings on \(\mathbb {B}_X\). We first show that α-Bloch spaces on \(\mathbb {B}_X\) are complex Banach spaces. Next, we give sufficient conditions for the composition operator from the α-Bloch space into the β-Bloch space to be bounded or compact. In the case that the α-Bloch space is a Bloch space, then these conditions are also necessary. Particular cases of interest will also be mentioned.
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