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 ( Γ ) . Nevertheless, when K is an Eberlein compact of finite height such that C ( K ) is not isomorphic to c 0 ( Γ ) , all isomorphism between subspaces of C ( K ) of size less than ℵ ω extend to automorphisms of C ( K ) .