On module maps and bilinear forms defined on shift-invariant subspaces of Lp(X)

AbstractIn this paper we prove a lifting of the commutant theorem on Lp(T; X) when X is a Banach space of type 2 and p ϵ [2, + ∞[. We also obtain a generalization of Sarason's lifting theorem. Then we study some modular versions of hilbertian factorizations for module maps between invariant subspaces of Lp(T; X). The last part of the paper is devoted to a representation theorem for invariant subspaces of H2(X) which are isomorphic to a Hilbert space