International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2749-2756
doi:10.1155/IJMMS.2005.2749
The Kreps-Yan theorem for L∞
D.B. Rokhlin
Faculty of Mechanics and Mathematics, Rostov State University, 5 Zorge Street, Rostov-on-Don 344090, Russia
Abstract
We prove the following version of the Kreps-Yan theorem. For any norm-closed convex cone C⊂L∞ such that C∩L+∞={0} and C⊃−L+∞, there exists a strictly positive continuous linear functional, whose restriction on C is nonpositive. The technique of the proof differs from the usual approach, applicable to a weakly Lindelöf Banach space.