Locally convex inductive limits of normed algebras
Alberto Arosio (1974)
Rendiconti del Seminario Matematico della Università di Padova
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Locally convex inductive limits of normed algebras
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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.