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

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.

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 Gdifferentiable 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.