Complemented Subspaces of Spaces of Multilinear Forms and Tensor Products1

Among other things, we show that Lq is isomorphic to a complemented subspace of the space of multilinear forms on Lp1 Lpn, where q 1 is given by 1 p1 1 pn 1 q 1. The proof strongly depends on the L - module structure of the spaces Lp