The Hereditary Dunford-Pettis Property For L1(E)

Abstract

A Banach Space E Is Said To Be Hereditarily Dunford-Pettis If All Of Its Closed Subspaces Have The Dunford-Pettis Property. In This Note We Prove That The Banach Space 11 (E), Of All Absolutely Summing Sequences In E With The Usual Norm, Is Hereditarily Dunford-Pettis If And Only If E Is Also.