On contractively complemented subspaces of separable L1-preduals

It is shown that for an Li-predual space X and a countable linearly independent subset of ext (B-X*) whose norm-closed linear span Y in X* is w*-closed, there exists a w*-continuous contractive projection from X* onto Y. This result combined with those of Pelczynski and Bourgain yields a simple proof of the Lazar-Lindenstrauss theorem that every separable L-1-predual with non-separable dual contains a contractively complemented subspace isometric to C(Delta), the Banach space of functions continuous on the Cantor discontinuum Delta. It is further shown that if X* is isometric to l(1) and (e*(n)) is a basis for X* isometrically equivalent to the usual fl-basis, then there exists a w*-convergent subsequence of (e*(mn)) of (e*(n)) such that the closed linear subspace of X* generated by the sequence (e*(m2n-1)) is the range of a w*-continuous contractive projection in X*. This yields a new proof of Zippin's result that c(0) is isometric to a contractively complemented subspace of X.