Operators on C[0,1] preserving copies of asymptotic l1 spaces

Given separable Banach spaces X, Y, Z and a bounded linear operator T:X -> Y, then T is said to preserve a copy of Z provided that there exists a closed linear subspace E of X isomorphic to Z and such that the restriction of T to E is an into isomorphism. It is proved that every operator on C([0,1]) which preserves a copy of an asymptotic l(1) space also preserves a copy of C([0,1]).