A l_1-predual which is not isometric to a quotient of C(alpha)
  About twenty years ago Johnson and Zippin showed that every separable L_1(mu)-predual was isometric to a quotient of C(Delta ), where Delta is the Cantor set. In this note we will show that the natural analogue of the theorem for l_1-preduals does not hold. We will show that there are many l_1-preduals which are not isometric to a quotient of any C(K)-space with K a countable compact metric space. We also prove some general results about the relationship between l_1-preduals and quotients of C(K)-spaces with K a countable compact metric space.   The results in this paper were presented at the Workshop on Banach Space Theory in Merida, Venezuela, January 1992. 
Dale E. Alspach