International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2749-2756
The Kreps-Yan theorem for
Faculty of Mechanics and Mathematics, Rostov State University, 5 Zorge Street, Rostov-on-Don 344090, Russia
Received 1 January 2005; Revised 11 June 2005
Copyright © 2005 D. B. Rokhlin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove the following version of the Kreps-Yan theorem. For any norm-closed convex cone such that and , there exists a strictly positive continuous linear functional, whose restriction on is nonpositive. The technique of the proof differs from the usual approach, applicable to a weakly Lindelöf Banach space.