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

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.