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Proceedings of the American Mathematical Society

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Banach spaces with biholomorphically equivalent unit balls are isomorphic

Authors: Wilhelm Kaup and Harald Upmeier
Journal: Proc. Amer. Math. Soc. 58 (1976), 129-133
MSC: Primary 32M05; Secondary 58C10, 46B05
MathSciNet review: 0422704
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Abstract: It is shown that in every complex Banach space $ E$ with open unit ball $ D \subset E$ there is a closed $ C$-linear subspace $ V \subset E$ such that $ V \cap D$ is the orbit of the origin $ 0 \in E$ under the group $ {\operatorname{Aut}}(D)$ of all biholomorphic automorphisms of $ D$. In particular two complex Banach spaces are isometrically equivalent if and only if their open unit balls are biholomorphically equivalent.

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Article copyright: © Copyright 1976 American Mathematical Society