Vol. 26, No. 3, 1968

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Universally well-capped cones

Leonard Asimow

Vol. 26 (1968), No. 3, 421–431

A closed convex cone P is said to be universally well-capped if it contains a compact convex subset B such that P B is convex and P = n=1nB. The compact convex sets which are universal caps of some cone are represented as the positive part of the unit ball of an ordered Banach dual space with the weak topology. A characterization, involving the directedness of the unit ball, is given of those ordered Banach spaces whose dual cones are universally well-capped. An application is made to the Choquet boundary theory for subspaces of continuous functions on a compact Hausdorff space.

Mathematical Subject Classification
Primary: 46.06
Received: 7 September 1967
Published: 1 September 1968
Leonard Asimow