On Banach spaces C(K) isomorphic to c₀(Γ)

Witold Marciszewski. "On Banach spaces C(K) isomorphic to c₀(Γ)." Studia Mathematica 156.3 (2003): 295-302. <http://eudml.org/doc/284565>.

@article{WitoldMarciszewski2003,
abstract = {We give a characterization of compact spaces K such that the Banach space C(K) is isomorphic to the space c₀(Γ) for some set Γ. As an application we show that there exists an Eberlein compact space K of weight $ω_\{ω\}$ and with the third derived set $K^\{(3)\}$ empty such that the space C(K) is not isomorphic to any c₀(Γ). For this compactum K, the spaces C(K) and $c₀(ω_\{ω\})$ are examples of weakly compactly generated (WCG) Banach spaces which are Lipschitz isomorphic but not isomorphic.},
author = {Witold Marciszewski},
journal = {Studia Mathematica},
keywords = { spaces; spaces; Eberlein compact; Lipschitz isomorphic},
language = {eng},
number = {3},
pages = {295-302},
title = {On Banach spaces C(K) isomorphic to c₀(Γ)},
url = {http://eudml.org/doc/284565},
volume = {156},
year = {2003},
}

TY - JOUR
AU - Witold Marciszewski
TI - On Banach spaces C(K) isomorphic to c₀(Γ)
JO - Studia Mathematica
PY - 2003
VL - 156
IS - 3
SP - 295
EP - 302
AB - We give a characterization of compact spaces K such that the Banach space C(K) is isomorphic to the space c₀(Γ) for some set Γ. As an application we show that there exists an Eberlein compact space K of weight $ω_{ω}$ and with the third derived set $K^{(3)}$ empty such that the space C(K) is not isomorphic to any c₀(Γ). For this compactum K, the spaces C(K) and $c₀(ω_{ω})$ are examples of weakly compactly generated (WCG) Banach spaces which are Lipschitz isomorphic but not isomorphic.
LA - eng
KW - spaces; spaces; Eberlein compact; Lipschitz isomorphic
UR - http://eudml.org/doc/284565
ER -