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, Enrico
Secondo
;
Piasecki, Lukasz
Ultimo
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.
2017
Inglese
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]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/98026
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 9
social impact