Lipschitz and uniform embeddings into $ℓ_{∞}$

• Autorzy: N. J. Kalton
• Języki publikacji: EN

Abstrakty

EN

We show that there is no uniformly continuous selection of the quotient map $Q: ℓ_{∞} → ℓ_{∞}/c₀$ 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 $B_X$.

Kategorie tematyczne

• 46T99: None of the above, but in this section
• 46B20: Geometry and structure of normed linear spaces
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 212
• Numer: 1
• Strony: 53-69

Daty

wydano

2011

Twórcy

autor

N. J. Kalton

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

Identyfikatory

DOI

10.4064/fm212-1-4