An Isomorphic Classification of $C(2^{𝔪} × [0,α])$ Spaces

• Autorzy: Elói Medina Galego
• Języki publikacji: EN

Abstrakty

EN

We present an extension of the classical isomorphic classification of the Banach spaces C([0,α]) of all real continuous functions defined on the nondenumerable intervals of ordinals [0,α]. As an application, we establish the isomorphic classification of the Banach spaces $C(2^{𝔪} × [0,α])$ of all real continuous functions defined on the compact spaces $2^{𝔪} × [0,α]$, the topological product of the Cantor cubes $2^{𝔪}$ with 𝔪 smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. Consequently, it is relatively consistent with ZFC that this yields a complete isomorphic classification of $C(2^{𝔪} × [0,α])$ spaces.

Kategorie tematyczne

• 03E55: Large cardinals
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: 57
• Numer: 3
• Strony: 279-287

Daty

wydano

2009

Twórcy

autor

Elói Medina Galego

• Department of Mathematics, University of São Paulo, São Paulo, Brazil 05508-090

Identyfikatory

DOI

10.4064/ba57-3-9