A construction of a Banach space C(K) with few operators

We present a construction, carried entirely in ZFC, of a compact connected space K such that every bounded operator T : C(K) --> C(K) can be written as T = g (.) l + S, where g is an element of C(K) and S is a weakly compact operator. This extends a result due to Koszmider [A Banach space of continuous functions with few operators, Preprint, 2003] who constructed such a space assuming the continuum hypothesis. (C) 2004 Elsevier B.V. All rights reserved.