Separable Lindenstrauss spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings
Studia Mathematica, Tome 238 (2017) no. 1, pp. 1-16
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\ell _1$. This result allows us to obtain a characterization of all separable Lindenstrauss spaces $X$ with $X^*$ failing the $w^*$-fixed point property.
Keywords:
study * fixed point property nonexpansive mappings first dual space * lacks * fixed point property whenever contains isometric copy nbsp main result paper provides several characterizations weak star topologies fail fixed point property nonexpansive mappings nbsp ell result allows obtain characterization separable lindenstrauss spaces * failing * fixed point property
Affiliations des auteurs :
Emanuele Casini 1 ; Enrico Miglierina 2 ; Łukasz Piasecki 3
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author = {Emanuele Casini and Enrico Miglierina and {\L}ukasz Piasecki},
title = {Separable {Lindenstrauss} spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings},
journal = {Studia Mathematica},
pages = {1--16},
publisher = {mathdoc},
volume = {238},
number = {1},
year = {2017},
doi = {10.4064/sm8237-12-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8237-12-2016/}
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Emanuele Casini; Enrico Miglierina; Łukasz Piasecki. Separable Lindenstrauss spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings. Studia Mathematica, Tome 238 (2017) no. 1, pp. 1-16. doi: 10.4064/sm8237-12-2016
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