a1 Department of Mathematics, University of Catania, Italy
We prove the following result: if a Banach space E does not contain l1 and F has the (RDPP), then E n F has the same property, provided that L(E, F*) = K(E, F*). Hence we prove that if E n F has the (RDPP) then at least one of the spaces E and F must not contain l1. Some corollaries are then presented as well as results concerning the necessity of the hypothesis L(E, F*) = K(E, F*).
(Received December 19 1989)
(Revised July 05 1990)