GENERALIZED DUALS OF UNCONDITIONAL SPACES AND LOZANOVSKII THEOREM

We consider products K. L of unconditional bodies in R(n). We prove th at if M is the unit ball of l(p), 1 less-than-or-equal-to p less-than- or-equal-to infinity, and K and L are unconditional bodies that are ma ximal subject to K. L subset-of M, then K. L = M. This generalizes Loz anovskii's theorem. We also construct an example to show that equality need not hold for a general unconditional body M. This leads to two n atural conjectures.