Vol. 34, No. 2, 1970

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ISSN: 0030-8730
Facial decomposition of linearly compact simplexes and separation of functions on cones

Leonard Asimow and Alan John Ellis

Vol. 34 (1970), No. 2, 301–309
Abstract

Necessary and sufficient conditions for a linearly compact simplex K to be uniquely decomposable at a face are given. If P is a cone having the Riesz decomposition property and if f,g are subadditive homogeneous functions on P with f g then it is shown that there is an additive homogeneous function h on P with f h g. If P is a lattice cone for the dual space of an ordered Banach space X and if f,g are also w-continuous then, under certain conditions, it is possible to choose h X; a consequence of this result is Andô’s theorem, that an ordered Banach space has the Riesz decomposition property if its dual space is a lattice. A nonmeasure theoretic proof of Edwards’ separation theorem for compact simplexes is also deduced from these results.

Mathematical Subject Classification
Primary: 46.06
Milestones
Received: 8 July 1969
Published: 1 August 1970
Authors
Leonard Asimow
Alan John Ellis