Kreps-Yan theorem for Banach ideal spaces

Mathematics – Functional Analysis

Scientific paper

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6 pages

Scientific paper

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.

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