An indecomposable Banach space of continuous functions which has small density

Volume 202 / 2009

Rogério Augusto dos Santos Fajardo Fundamenta Mathematicae 202 (2009), 43-63 MSC: Primary 03E35; Secondary 46E15, 46E20, 46E26. DOI: 10.4064/fm202-1-2


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 $\omega _1<2^\omega $ 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.


  • Rogério Augusto dos Santos FajardoInstituto de Matemática e Estatística
    Universidade de São Paulo
    Rua do Matão, 1010
    CEP 05508-900 São Paulo, SP, Brazil

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