Some remarks on universality properties of ${\ell }_{\infty }/c₀$

Mikołaj Krupski, and Witold Marciszewski. "Some remarks on universality properties of $ℓ_∞/c₀$." Colloquium Mathematicae 128.2 (2012): 187-195. <http://eudml.org/doc/283939>.

@article{MikołajKrupski2012,
abstract = {We prove that if is not a Kunen cardinal, then there is a uniform Eberlein compact space K such that the Banach space C(K) does not embed isometrically into $ℓ_∞/c₀$. We prove a similar result for isomorphic embeddings. Our arguments are minor modifications of the proofs of analogous results for Corson compacta obtained by S. Todorčević. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $ℓ_∞/c₀$, but fails to embed isometrically. As far as we know it is the first example of this kind.},
author = {Mikołaj Krupski, Witold Marciszewski},
journal = {Colloquium Mathematicae},
keywords = { spaces; uniform Eberlein compact; Kunen cardinal; universal space},
language = {eng},
number = {2},
pages = {187-195},
title = {Some remarks on universality properties of $ℓ_∞/c₀$},
url = {http://eudml.org/doc/283939},
volume = {128},
year = {2012},
}

TY - JOUR
AU - Mikołaj Krupski
AU - Witold Marciszewski
TI - Some remarks on universality properties of $ℓ_∞/c₀$
JO - Colloquium Mathematicae
PY - 2012
VL - 128
IS - 2
SP - 187
EP - 195
AB - We prove that if is not a Kunen cardinal, then there is a uniform Eberlein compact space K such that the Banach space C(K) does not embed isometrically into $ℓ_∞/c₀$. We prove a similar result for isomorphic embeddings. Our arguments are minor modifications of the proofs of analogous results for Corson compacta obtained by S. Todorčević. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $ℓ_∞/c₀$, but fails to embed isometrically. As far as we know it is the first example of this kind.
LA - eng
KW - spaces; uniform Eberlein compact; Kunen cardinal; universal space
UR - http://eudml.org/doc/283939
ER -