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Holomorphic functions on strict inductive limits of Banach spaces. (English) Zbl 0789.46039

Summary: We show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.

MSC:

46G20 Infinite-dimensional holomorphy
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
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