Bounded analytic sets in Banach spaces

Aurich, Volker

Annales de l'Institut Fourier, Tome 36 (1986) no. 4, pp. 229-243.

Des conditions sont présentées pour qu’un espace analytique $X$ soit ou ne soit pas isomorphe à un sous-ensemble analytique fermé et borné d’un espace de Banach. Elles comprennent d’une part la propriété de Radon-Nikodym et d’autre part la métrique de Caratheodory.

Conditions are given which enable or disable a complex space $X$ to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of $X$.

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