This is an announcement for the paper "The Kreps-Yan theorem for $L^\infty$" by Dmitry B. Rokhlin.
Abstract: We prove the following version of the Kreps-Yan theorem. For any norm closed convex cone $C\subset L^\infty$ such that $C\cap L_+^\infty={0}$ and $C\supset -L_+^\infty$, there exists a strictly positive continuous linear functional, whose restriction on $C$ is non-positive. The proof uses some tools from convex analysis in contrast to the case of a weakly Lindel"of Banach space, where such approach is not needed.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46E30; 46B40
Remarks: 8 pages
The source file(s), rok_KY.TEX: 18051 bytes, is(are) stored in gzipped form as 0412551.gz with size 7kb. The corresponding postcript file has gzipped size 45kb.
Submitted from: rokhlin@math.rsu.ru
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