Automorphisms in spaces of continuous functions on Valdivia compacta

We show that there are no automorphic Banach spaces of the form C(K) with K continuous image of Valdivia compact except the spaces c(0)(Gamma). Nevertheless, when K is an Eberlein compact of finite height such that C(K) is not isomorphic to c(0)(Gamma), all isomorphism between subspaces of C(K) of size less than aleph(omega) extend to automorphisms of C(K). (C) 2008 Elsevier B.V. All rights reserved.