An alternative Dunford-Pettis Property

Tom 125 / 1997

Walden Freedman Studia Mathematica 125 (1997), 143-159 DOI: 10.4064/sm-125-2-143-159


An alternative to the Dunford-Pettis Property, called the DP1-property, is introduced. Its relationship to the Dunford-Pettis Property and other related properties is examined. It is shown that $ℓ_p$-direct sums of spaces with DP1 have DP1 if 1 ≤ p < ∞. It is also shown that for preduals of von Neumann algebras, DP1 is strictly weaker than the Dunford-Pettis Property, while for von Neumann algebras, the two properties are equivalent.


  • Walden Freedman

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