# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## An indecomposable Banach space of continuous functions which has small density

### Tom 202 / 2009

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

#### Streszczenie

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.

#### Autorzy

• Rogério Augusto dos Santos FajardoInstituto de Matemática e Estatística