no. 11
Functional analysis/Geometry
Uniform nonextendability from nets
[Impossibilité d'extension uniforme depuis les réseaux]

Présenté par : Gilles Pisier

Naor, Assaf1
1 Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA
Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 991-994.

On montre qu'il existe des espaces de Banach X,Y, un réseau N de X et une application lipschitzienne f:N→Y telle qu'aucune extension F:X→Y de f n'est uniformément continue.

It is shown that there exist Banach spaces X,Y, a 1-net N of X and a Lipschitz function f:N→Y such that every F:X→Y that extends f is not uniformly continuous.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.09.005
Naor, Assaf 1

1 Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA 
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Naor, Assaf. Uniform nonextendability from nets. Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 991-994. doi : 10.1016/j.crma.2015.09.005. http://www.numdam.org/articles/10.1016/j.crma.2015.09.005/

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