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.
