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(a)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(a)arXiv.org.
