An alternative Dunford-Pettis Property

Walden Freedman

ArticleOriginal scientific text

Title

An alternative Dunford-Pettis Property

Authors ^1,²

Affiliations

Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106, U.S.A.
Department of Mathematics, Eastern Mediterranean University, Gazimağusa, TRNC, Mersin 10, Turkey

Abstract

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.

Keywords

ENG

Dunford-Pettis Property, Kadec-Klee Property

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Title

An alternative Dunford-Pettis Property

Affiliations

Abstract

Keywords

Bibliography