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On the isometries of $ H\sp \infty\sb E(B)$

Authors: Yasuo Matsugu and Takahiko Yamada
Journal: Proc. Amer. Math. Soc. 120 (1994), 1107-1112
MSC: Primary 46E40; Secondary 47B38
MathSciNet review: 1169883
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Abstract: Let $ E$ be a complex Banach space on which all the multipliers are trivial. Let $ H_E^\infty (B)$ denote the Banach space of $ E$-valued bounded holomorphic functions on the open unit ball $ B$ of $ {{\mathbf{C}}^n}$. In this paper we prove that every linear isometry $ T$ of $ H_E^\infty (B)$ onto itself is of the form $ (TF)(z) = \mathfrak{T}F(\varphi (z))$ for all $ F \in H_E^\infty (B),\;z \in B$, where $ \mathfrak{T}$ is a linear isometry of $ E$ onto itself and $ \varphi $ is a biholomorphic map of $ B$.

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