非扩张映象的可分Lindenstrauss空间的弱$^*$不动点性质
Separable Lindenstrauss spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings
摘要：
本文研究了非扩张映象的$w^*$ -不动点性质。首先证明了当$X$包含空间$c$的等距拷贝时，对偶空间$X^*$缺乏$w^*$ -不动点性质.然后，本文的主要结果给出了$\ell_1$空间中非扩张映射不具有不动点性质的弱 * 拓扑的几个刻画。这一结果使我们得到了所有可分Lindenstrauss空间$X$的一个特征，从而导致了$X^*$中$w^*$ -不动点性质的失效.
英文摘要：
In this paper we study the $w^*$-fixed point property for nonexpansive mappings. First we show that the dual space $X^*$ lacks the $w^*$-fixed point property whenever $X$ contains an isometric copy of the space $c$. Then, the main result of our paper provides several characterizations of weak-star topologies that fail the fixed point property for nonexpansive mappings in $\ell_1$ space. This result allows us to obtain a characterization of all separable Lindenstrauss spaces $X$ inducing the failure of $w^*$-fixed point property in $X^*$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
