Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On the reciprocal Dunford-Pettis property in projective tensor products

G. Emmanuelea1

a1 Department of Mathematics, University of Catania, Italy

Abstract

We prove the following result: if a Banach space E does not contain l1 and F has the (RDPP), then E xs2297n F has the same property, provided that L(E, F*) = K(E, F*). Hence we prove that if E xs2297n 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)