On a one-sided James' theorem

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• 作者：Warren B. Moors ^{moors@math.auckland.ac.nz}
• 关键词：Weakly compact sets ; James' theorem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：528-530
• 全文大小：199 K
• 卷排序：449

文摘

We provide a short proof of the following fact: If X is a Banach space, A and B   are bounded, closed and convex sets with dist(A,B)>0dist(A,B)>0 and every x⁎∈X⁎x⁎∈X⁎ with the property that sup⁡(x⁎,B)<inf⁡(x⁎,A)sup⁡(x⁎,B)<inf⁡(x⁎,A) attains its infimum on A and its supremum on B, then both A and B are weakly compact.