2016/04/26 by Emanuele Casini, Enrico Miglierina, Casini, Emanuele +5
Mathematics · #46B25 #46B45 #47H10 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B25 #msc:46B45 #msc:47H10
paper · pdf · doi:10.48550/arxiv.1604.07587
arxiv created 2016/11/04 · arxiv updated 2016/11/07
The aim of this paper is to study the w^*-fixed point property for nonexpansive mappings in the duals of separable Lindenstrauss spaces by means of suitable geometrical properties of the dual ball. First we show that a property concerning the behaviour of a class of w^*-closed subsets of the dual sphere is equivalent to the w^*-fixed point property. Then, the main result of our paper shows an equivalence between another, stronger geometrical property of the dual ball and the stable w^*-fixed point property. The last geometrical notion was introduced by Fonf and Veselý as a strengthening of the notion of polyhedrality. In the last section we show that also the first geometrical assumption that we have introduced can be related to a polyhedral concept for the predual space. Indeed, we give a hierarchical structure among various polyhedrality notions in the framework of Lindenstrauss spaces. Finally, as a by-product, we obtain an improvement of an old result about the norm-preserving compact extension of compact operators.