First we prove that if a separable Banach space X contains an isometric copy of an infinite-dimensional space A(S) of affine continuous functions on a Choquet simplex S, then its dual X* lacks the weak* fixed point property for nonexpansive mappings. Then, we show that the dual of a separable L1-predual X fails the weak* fixed point property for nonexpansive mappings if and only if X has a quotient isometric to some infinite-dimensional space A(S). Moreover, we provide an example showing that “quotient” cannot be replaced by “subspace”. Finally, it is worth mentioning that in our characterization the space A(S) cannot be substituted by any space C(K) of continuous functions on a compact Hausdorff K.

Weak* fixed point property and the space of affine functions

Casini E.;Miglierina E.
;
2021

Abstract

First we prove that if a separable Banach space X contains an isometric copy of an infinite-dimensional space A(S) of affine continuous functions on a Choquet simplex S, then its dual X* lacks the weak* fixed point property for nonexpansive mappings. Then, we show that the dual of a separable L1-predual X fails the weak* fixed point property for nonexpansive mappings if and only if X has a quotient isometric to some infinite-dimensional space A(S). Moreover, we provide an example showing that “quotient” cannot be replaced by “subspace”. Finally, it is worth mentioning that in our characterization the space A(S) cannot be substituted by any space C(K) of continuous functions on a compact Hausdorff K.
L; 1; -preduals; Nonexpansive mappings; Spaces of affine functions; Spaces of continuous functions; W; *; fixed point property
Casini, E.; Miglierina, E.; Piasecki, L.
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: http://hdl.handle.net/11383/2113952
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact