For Banach spaces $X$ and $Y$ we study the vector-valued spectrum $\mathcal M_\infty(B_X,B_Y)$, that is the set of non null algebra homomorphisms from $\mathcal H^\infty(B_X)$ to $\mathcal H^\infty(B_Y)$, which is naturally projected onto the closed unit ball of $\mathcal H^\infty(B_Y, X^{**})$. The aim of this article is to describe the fibers defined by this projection, searching for analytic balls and considering Gleason parts.

中文翻译：

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矢量值谱的纤维化描述

对于 Banach 空间 $X$ 和 $Y$，我们研究向量值谱 $\mathcal M_\infty(B_X,B_Y)$，即 $\mathcal H^\infty(B_X) 的一组非空代数同态$ 到 $\mathcal H^\infty(B_Y)$，自然投影到 $\mathcal H^\infty(B_Y, X^{**})$ 的闭合单位球上。本文的目的是描述由该投影定义的纤维，搜索解析球并考虑 Gleason 零件。