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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.FAPESP[04/03508-6]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

An indecomposable Banach space of continuous functions which has small density