We prove that, as in the finite dimensional case, the space of Bloch functions on the unit ball of a Hilbert space contains, under very mild conditions, any semi-Banach space of analytic functions invariant under automorphisms. The multipliers for such Bloch space are characterized and some of their spectral properties are described.

中文翻译：

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希尔伯特空间单位球上的布洛赫空间：极大值和乘数

我们证明，与有限维情况一样，希尔伯特空间的单位球上的Bloch函数空间在非常温和的条件下包含自同构不变的任何解析函数半Banach空间。表征了此类Bloch空间的乘法器，并描述了其某些光谱特性。