An indecomposable Banach space of continuous functions which has small density

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

Abstrakty

EN

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight $ω₁ < 2^{ω}$ such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46E20: Hilbert spaces of continuous, differentiable or analytic functions
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 202
• Numer: 1
• Strony: 43-63

Daty

wydano

2009

Twórcy

autor

Rogério Augusto dos Santos Fajardo

• Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-900 São Paulo, SP, Brazil

Identyfikatory

DOI

10.4064/fm202-1-2