Complemented Subspaces and Interpolation Properties in Spaces of Polynomials

AbstractLetXbe a Banach space whose dualX* has typep∈(1,2]. Ifmis an integer greater thanp/(p−1) and (xn) is a seminormalized sequence weakly convergent to zero, there is a subsequence (yn) of (xn) such that, for each element (an) ofl∞, there is anm-homogeneous continuous polynomialPonXwithP(yn)=an,n=1,2,…. Some interpolation and complementation properties are also given in P(mlp), form