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

Dineen, Seán

Math. Scand. 59, 131-142 (1986).

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

Keywords:

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; ultraproduct of \(JB^ *\) triple systems; bidual; biholomorphic automorphisms