Vol. 34, No. 2, 1970

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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

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
Received: 8 July 1969
Published: 1 August 1970
Leonard Asimow
Alan John Ellis