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.
Lingua originale | English |
---|---|
pagine (da-a) | 1613-1620 |
Numero di pagine | 8 |
Rivista | Proceedings of the American Mathematical Society |
Volume | 149 |
DOI | |
Stato di pubblicazione | Pubblicato - 2021 |
Keywords
- L_1-preduals
- nonexpansive mappings
- spaces of affine functions
- spaces of continuous functions
- w^* fixed point property