Mathematics – Functional Analysis
Scientific paper
2008-04-14
Mathematics
Functional Analysis
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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