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We show that there are no automorphic Banach spaces of the form C(K) with Kcontinuous image of Valdivia compact except the spaces c0(I). Nevertheless,when K is an Eberlein compact of finite height such that C(K) is not isomorphicto c0(I), all isomorphism between subspaces of C(K) of size less thanaleph_omega extend to automorphisms of C(K).

Automorphisms in spaces of continuous functions on Valdivia compacta