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 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. This result allows us to obtain a characterization of all separable Lindenstrauss spaces X with X∗failing the w∗-fixed point property.
Separable Lindenstrauss spaces whose duals lack the weak∗ fixed point property for nonexpansive mappings
CASINI, EMANUELE GIUSEPPE;
2017-01-01
Abstract
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 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. This result allows us to obtain a characterization of all separable Lindenstrauss spaces X with X∗failing the w∗-fixed point property.
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