Kreps-Yan theorem for Banach ideal spaces

TL;DR

This paper extends the Kreps-Yan theorem to Banach ideal spaces, establishing conditions for the existence of positive functionals related to convex cones, which has implications in functional analysis and financial mathematics.

Contribution

It proves a Kreps-Yan type theorem for Banach ideal spaces, linking cone conditions to the existence of positive continuous functionals.

Findings

Conditions for cones imply existence of positive functionals

Extension of Kreps-Yan theorem to Banach ideal spaces

Provides a functional-analytic framework for cone conditions

Abstract

Let $C$ be a closed convex cone in a Banach ideal space $X$ on a measurable space with a $\sigma$-finite measure. We prove that conditions $C\cap X_+=\{0\}$ and $C\supset -X_+$ imply the existence of a strictly positive continuous functional on $X$, whose restriction to $C$ is non-positive.