Displaying similar documents to “On sequences not enjoying Schur’s property”

On the class of b-L-weakly and order M-weakly compact operators

Driss Lhaimer, Mohammed Moussa, Khalid Bouras (2020)

Mathematica Bohemica

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In this paper, we introduce and study new concepts of b-L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of KB-spaces.

An alternative Dunford-Pettis Property

Walden Freedman (1997)

Studia Mathematica

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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.

Polynomial characterizations of the Dunford-Pettis property.

Manuel González, Joaquín M. Gutiérrez (1991)

Extracta Mathematicae

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We introduce and characterize the class P of polynomials between Banach spaces whose restrictions to Dunford-Pettis (DP) sets are weakly continuous. All the weakly compact and the scalar valued polynomials belong to P. We prove that a Banach space E has the Dunford-Pettis (DP) property if and only if every P ∈ P is weakly sequentially continuous. This result contains a characterization of the DP property given in [3], answering a question of Pelczynski: E has the DP property if and only...

On the class of order almost L-weakly compact operators

Kamal El Fahri, Hassan Khabaoui, Jawad Hmichane (2022)

Commentationes Mathematicae Universitatis Carolinae

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We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem.