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·I+S, where g∈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.