On subspaces of c(0) and extension of operators into C(K)-spaces

Johnson and Zippin recently showed that if X is a weak*-closed subspace of l(1) and T : X --> C(K) is any bounded operator then T can be extended to a bounded operator T : l(1) --> C(K). We give a converse result: if X is a s ubspace of l(1) such that l(1)/X has an unconditional finite-dimensional de composition (UFDD) and every operator T : X --> C (K) can be extended to l( 1) then there is an automorphism tau of l(1) such that tau (X) is weak*-clo sed. This result is proved by studying subspaces of c(0) and several differ ent characterizations of such subspaces are given.