Year: 2004
Type: preprint
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 Lindelöf Banach space, where such approach is not needed.
Source: arXiv (Cornell University)
Author: Rokhlin, Dmitry B.
Institution: Southern Federal University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1619901466