## 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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