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arXiv · 1610.02763

Conic James' Compactness Theorem

J. Orihuela
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Abstract

Our main result is the following: {\it Let $E$ be a Banach space and $D$ be a weakly compact subset of $E$ with $0\notin D$. If $A$ is a bounded subset of $E$ such that every $x^*\in E^*$ with $x^*(D) >0$ attains its supremum on $A$, then $A$ is weakly relatively compact.}

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J. Orihuela. 2016-10-10. Conic James' Compactness Theorem. https://arxiv.org/abs/1610.02763

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