强超弱紧生成Banach空间不动点性质

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张吉超,张文.强超弱紧生成Banach空间不动点性质[J].,2017,57(1):100-104

强超弱紧生成Banach空间不动点性质

Fixed-point property of strongly super weakly compact generated Banach spaces

DOI：10.7511/dllgxb201701014

中文关键词:超弱紧集不动点性质 Banach空间

英文关键词:super weakly compact set fixed-point property Banach space

基金项目:国家自然科学基金资助项目(11471270)；福建省自然科学基金资助项目(2015J01022)；厦门大学校长基金资助项目(20720160010).

作者	单位
张吉超,张文

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中文摘要:

主要研究Banach空间的不动点性质,并给出一种全新的证明方法.首先利用超幂方法证明范数一致 G 光滑在凸集本身以及它的超幂上是相等的，然后利用反证法证明凸集在范数一致 G 光滑下对非扩张映射具有不动点性质,最后证明了每个强超弱紧生成的Banach空间在再赋范意义下满足每个弱紧凸集具有超不动点性质．

英文摘要:

The fixed-point property of Banach space is studied and a new proof method is given. Firstly, the ultraproduct method is used to prove that the uniformly G -differentiable norms are equivalent under convex sets and its ultraproduct. Then, by means of counter-proof, it is proven that convex sets have the fixed-point property for nonexpansive mappings under the uniformly G -differentiable norm sense. Finally, it is shown that every strongly super weakly compact generated Banach space can be renormed so that every weakly compact convex set has super fixed-point property.

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强超弱紧生成Banach空间不动点性质

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