Abstract
In this note we introduce the notion of smooth module to extend results from homology theory of Banach algebras to the locally convex category. A complete locally convex module over an m-convex algebra is shown to be smooth if and only if it is topologically isomorphic to a reduced inverse limit of Banach modules over Banach algebras. Stability properties for smoothness are discussed and conditions under which an arbitrary locally convex module is rendered smooth are given.
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