Best constants for Lipschitz embeddings of metric spaces into $c_0$

Tom 199 / 2008

N. J. Kalton, G. Lancien Fundamenta Mathematicae 199 (2008), 249-272 MSC: Primary 46B20; Secondary 46T99. DOI: 10.4064/fm199-3-4

Streszczenie

We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into $c_0$ and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical $\ell _p$-spaces into $c_0$ and give other applications. We prove that if a Banach space embeds almost isometrically into $c_0$, then it embeds linearly almost isometrically into $c_0$. We also study Lipschitz embeddings into $c_0^+$.

Autorzy

  • N. J. KaltonDepartment of Mathematics
    University of Missouri-Columbia
    Columbia, MO 65211, U.S.A.
    e-mail
  • G. LancienLaboratoire de Mathématiques UMR 6623
    Université de Franche-Comté
    16 route de Gray
    25030 Besançon Cedex, France
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek