manuscripta mathematica

, Volume 45, Issue 1, pp 61–67

Bounded holomorphic embeddings of the unit disk into Banach spaces

  • Volker Aurich

DOI: 10.1007/BF01168580

Cite this article as:
Aurich, V. Manuscripta Math (1983) 45: 61. doi:10.1007/BF01168580


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/H01 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.

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Volker Aurich
    • 1
  1. 1.Mathematisches Institut derLudwig-Maximilians-UniversitätMünchen 2West Germany