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

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