Banach-valued Bloch-type functions on the unit ball of a Hilbert space and weak spaces of Bloch-type

Year 2023, Volume: 6 Issue: 1, 6 - 21, 15.03.2023

Thai Quang

https://doi.org/10.33205/cma.1243686

Cited By: 2

Abstract

In this article, we study the space $\mathcal B_\mu(B_X,Y)$ of $Y$-valued Bloch-type functions on the unit ball $B_X$ of an infinite dimensional Hilbert space $X$ with $\mu$ is a normal weight on $B_X$ and $Y$ is a Banach space. We also investigate the characterizations of the space $\mathcal{WB}_\mu(B_X)$ of $Y$-valued, locally bounded, weakly holomorphic functions associated with the Bloch-type space $\mathcal B_\mu(B_X)$ of scalar-valued functions in the sense that $f\in \mathcal{WB}_\mu(B_X)$ if $w\circ f \in \mathcal B_\mu(B_X)$ for every $w \in \mathcal W,$ a separating subspace of the dual $Y'$ of $Y.$

Keywords

Operators on Hilbert spaces, Bloch spaces, Weak holomorphic

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