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.
Casini, E., Miglierina, E., Piasecki, L., Separable Lindenstrauss spaces whose duals lack the weak∗ fixed point property for nonexpansive mappings, <<STUDIA MATHEMATICA>>, 2017; 238 (1): 1-16. [doi:10.4064/sm8237-12-2016] [http://hdl.handle.net/10807/98026]
Separable Lindenstrauss spaces whose duals lack the weak∗ fixed point property for nonexpansive mappings
Miglierina, EnricoSecondo
;Piasecki, LukaszUltimo
2017
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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