Lipschitz and uniform embeddings into ${\ell }_{\infty }$

N. J. Kalton. "Lipschitz and uniform embeddings into $ℓ_{∞}$." Fundamenta Mathematicae 212.1 (2011): 53-69. <http://eudml.org/doc/283253>.

@article{N2011,
abstract = {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 $B_X$.},
author = {N. J. Kalton},
journal = {Fundamenta Mathematicae},
keywords = {uniform selections; Lipschitz selections; uniform retractions; Lipschitz retractions; uniform embeddings; Lipschitz embeddings; Banach lattices; Arens-Eells space},
language = {eng},
number = {1},
pages = {53-69},
title = {Lipschitz and uniform embeddings into $ℓ_\{∞\}$},
url = {http://eudml.org/doc/283253},
volume = {212},
year = {2011},
}

TY - JOUR
AU - N. J. Kalton
TI - Lipschitz and uniform embeddings into $ℓ_{∞}$
JO - Fundamenta Mathematicae
PY - 2011
VL - 212
IS - 1
SP - 53
EP - 69
AB - 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 $B_X$.
LA - eng
KW - uniform selections; Lipschitz selections; uniform retractions; Lipschitz retractions; uniform embeddings; Lipschitz embeddings; Banach lattices; Arens-Eells space
UR - http://eudml.org/doc/283253
ER -