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An alternative Dunford-Pettis Property

100%

Freedman W.

Studia Mathematica

1997

tom 125

nr 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.

An extension property for Banach spaces

100%

Freedman W.

Colloquium Mathematicum

2002

tom 91

nr 2

167-182

A Banach space X has property (E) if every operator from X into c₀ extends to an operator from X** into c₀; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties, and the property of being a Grothendieck space.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Freedman W.

1 2002

1 1997

Wyniki wyszukiwania

An alternative Dunford-Pettis Property

An extension property for Banach spaces