On the complemented subspaces ofX p

In this paper we prove some results related to the problem of isomorphically classifying the complemented subspaces ofX _p.We characterize the complemented subspaces ofX _pwhich are isomorphic toX _pby showing that such a space must contain a canonical complemented subspace isomorphic toX _p.We also give some characterizations of complemented subspaces ofX _pisomorphic tol _p⊕l ₂. Research supported in part by NSF grant DMS 890237.