Lipschitz and uniform embeddings into $ℓ_{∞}$

N. J. Kalton

Lipschitz and uniform embeddings into

ℓ_{\infty}

N. J. Kalton

Fundamenta Mathematicae, Tome 215 (2011), p. 53-69 / Harvested from The Polish Digital Mathematics Library

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Résumé

We show that there is no uniformly continuous selection of the quotient map $Q : ℓ_{\infty} \to ℓ_{\infty} / c ₀$ 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 $B_{X}$ .

Publié le : 2011-01-01

Zbl 1220.46014

EUDML-ID : urn:eudml:doc:283253

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N. J. Kalton. Lipschitz and uniform embeddings into $ℓ_{∞}$
            . Fundamenta Mathematicae, Tome 215 (2011) pp. 53-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-1-4/