Geodesic
Lipschitz and uniform embeddings into $\ell _{\infty} $
N. J. Kalton1
1 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A.
Fundamenta Mathematicae, Tome 212 (2011) no. 1, pp. 53-69.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that there is no uniformly continuous selection of the quotient map $Q:\ell _\infty \to \ell _\infty //c_0$ relative to the unit ball. We use this to construct an answer to a problem of Benyamini and Lindenstrauss; there is a Banach space $X$ such that there is a no Lipschitz retraction of $X^{**}$ onto $X$; in fact there is no uniformly continuous retraction from $B_{X^{**}}$ onto $B_X$.
DOI : 10.4064/fm212-1-4
Mots-clés : there uniformly continuous selection quotient map ell infty ell infty relative unit ball construct answer problem benyamini lindenstrauss there banach space there lipschitz retraction ** there uniformly continuous retraction **

N. J. Kalton 1

1 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A. 
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N. J. Kalton. Lipschitz and uniform embeddings into $\ell _{\infty} $. Fundamenta Mathematicae, Tome 212 (2011) no. 1, pp. 53-69. doi : 10.4064/fm212-1-4. http://geodesic.mathdoc.fr/articles/10.4064/fm212-1-4/

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