Abstract of a paper by Dmitry B. Rokhlin
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0412551 or http://arXiv.org/abs/math.FA/0412551 or by email in unzipped form by transmitting an empty message with subject line uget 0412551 or in gzipped form by using subject line get 0412551 to: math@arXiv.org.
participants (1)
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Dale Alspach