AN ALTERNATIVE DUNFORD-PETTIS PROPERTY

An alternative to the Dunford-Pettis Property, called the DP1-property , is introduced. Its relationship to the Dunford-Pettis Property and o ther related properties is examined. It is shown that e(p)-direct sums of spaces with DP1 have DP1 if I less than or equal to p < infinity. It is also shown that for preduals of von Neumann algebras, DP1 is str ictly weaker than the Dunford-Pettis Property, while for von Neumann a lgebras, the two properties are equivalent.