Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains

Sean Dineen

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Holomorphic functions on strict inductive limits of Banach spaces.

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In this article 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.

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