Essentially Incomparable Banach Spaces of Continuous Functions

• Autorzy: Rogério Augusto dos Santos Fajardo
• Języki publikacji: EN

Abstrakty

EN

We construct, under Axiom ♢, a family $(C(K_ξ))_{ξ<2^{(2^ω)}}$ of indecomposable Banach spaces with few operators such that every operator from $C(K_ξ)$ into $C(K_η)$ is weakly compact, for all ξ ≠ η. In particular, these spaces are pairwise essentially incomparable.
Assuming no additional set-theoretic axiom, we obtain this result with size $2^ω$ instead of $2^{(2^ω)}$.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46B20: Geometry and structure of normed linear spaces
• 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: 2010
• Tom: 58
• Numer: 3
• Strony: 247-258

Daty

wydano

2010

Twórcy

autor

Rogério Augusto dos Santos Fajardo

• Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Rua Arlindo Bettio, 1000, São Paulo, SP, Brazil

Identyfikatory

DOI

10.4064/ba58-3-7