Separable Lindenstrauss spaces whose duals lack the weak^* fixed point property for nonexpansive mappings

2015/03/30 by Emanuele Casini, Casini, Emanuele, Enrico Miglierina +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47H09 #Secondary 46B25 #math.FA #msc:46B25 #msc:47H09

paper · pdf · doi:10.48550/arxiv.1503.08875

arxiv created 2015/03/30 · arxiv updated 2015/04/01

Abstract

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 ℓ₁ 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^*.

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