Quotients of indecomposable Banach spaces of continuous functions

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

Abstrakty

EN

Assuming ⋄, we construct a connected compact topological space K such that for every closed L ⊂ K the Banach space C(L) has few operators, in the sense that every operator on C(L) is multiplication by a continuous function plus a weakly compact operator. In particular, C(K) is indecomposable and has continuum many non-isomorphic indecomposable quotients, and K does not contain a homeomorphic copy of βℕ.
Moreover, assuming CH we construct a connected compact K where C(K) has few operators and K contains a homeomorphic copy of βℕ.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 03E65: Other hypotheses and axioms
• 54D05: Connected and locally connected spaces (general aspects)
• 46B26: Nonseparable Banach spaces
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 212
• Numer: 3
• Strony: 259-283

Daty

wydano

2012

Twórcy

autor

Rogério Augusto dos Santos Fajardo

• Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, Brazil

Identyfikatory

DOI

10.4064/sm212-3-4