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Bounded holomorphic embeddings of the unit disk into Banach spaces

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Abstract

It is shown that, in contrast to ℂn, infinite dimensional complex Banach spaces E can possess bounded complex closed submanifolds of positive dimension. If E contains c0 or L1/H 10 then the unit disk D can be embedded into E as a bounded complex closed submanifold. If, however, E has the analytic Radon-Nikodym property then no bounded embedding exists. Acknowledgement: I thank W. Hensgen and M. Schottenloher for many stimulating discussions.

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  1. Mathematisches Institut der, Ludwig-Maximilians-Universität, Theresienstraße 39, D-8000, München 2, West Germany

    Volker Aurich

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  1. Volker Aurich
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Aurich, V. Bounded holomorphic embeddings of the unit disk into Banach spaces. Manuscripta Math 45, 61–67 (1983). https://doi.org/10.1007/BF01168580

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