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Complete holomorphic vector fields on the second dual of a Banach space. (English) Zbl 0625.46055

It is shown that any uniformly bounded collection of complete holomorphic vector fields on the unit ball of Banach spaces can be combined to define such a vector field on the unit ball of any ultraproduct of the Banach spaces. As corollaries it is deduced that the ultraproduct of \(JB^*\) triple systems and the bidual of such a system are \(JB^*\) triple systems, and that biholomorphic automorphisms of the unit ball of a Banach space extend to such maps on the unit ball of the bidual.
Reviewer: A.Kriegl

MSC:

46G20 Infinite-dimensional holomorphy
46H70 Nonassociative topological algebras
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