Vol. 65, No. 2, 1976

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Geometry and the Radon-Nikodym theorem in strict Mackey convergence spaces

David Sexton Gilliam

Vol. 65 (1976), No. 2, 353–364

The main purpose of this paper is to indicate a technique for extending certain types of results which are known for Banach spaces to the corresponding results in more general locally convex topological vector spaces. We shall extend these results to the class of locally convex spaces possessing the strict Mackey convergence [SMC] property. The technique involves a natural embedding into a Banach space and an application of the Banach space result. Loosely speaking, we have that those properties of closed bounded sets in Banach spaces that do not depend upon any open set will yield analogous results for closed bounded sets in quasicomplete locally convex spaces with the SMC property.

Mathematical Subject Classification 2000
Primary: 46A05, 46A05
Secondary: 46G10
Received: 15 December 1975
Published: 1 August 1976
David Sexton Gilliam