, Volume 45, Issue 1, pp 61-67

Bounded holomorphic embeddings of the unit disk into Banach spaces

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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 0 1 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.