Complemented Subspaces and Interpolation Properties in Spaces of Polynomials

Let X be a Banach space whose dual X* has type pg 1, 2x. If m is an integer greater than pr py1.and xn.is a seminormalized sequence weakly convergent to zero, there is a subsequence yn.of xn.such that, for each element an.of l`, there is an m-homogeneous continuous polynomial P on X with P yn.san, ns1, 2, . . . . Some interpolation and complementation properties are also given in P mlp., for m-p, as well as in other spaces of polynomials and multilinear functionals