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

• Autorzy: Witold Marciszewski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 156
• Numer: 3
• Strony: 295-302

Daty

wydano

2003

Twórcy

autor

Witold Marciszewski

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm156-3-6