Displaying similar documents to “On the class of order Dunford-Pettis operators”

Completely Continuous operators

Ioana Ghenciu, Paul Lewis (2012)

Colloquium Mathematicae

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A Banach space X has the Dunford-Pettis property (DPP) provided that every weakly compact operator T from X to any Banach space Y is completely continuous (or a Dunford-Pettis operator). It is known that X has the DPP if and only if every weakly null sequence in X is a Dunford-Pettis subset of X. In this paper we give equivalent characterizations of Banach spaces X such that every weakly Cauchy sequence in X is a limited subset of X. We prove that every operator T: X → c₀ is completely...

A stronger Dunford-Pettis property

H. Carrión, P. Galindo, M. L. Lourenço (2008)

Studia Mathematica

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We discuss a strong version of the Dunford-Pettis property, earlier named (DP*) property, which is shared by both ℓ₁ and ℓ ∞ . It is equivalent to the Dunford-Pettis property plus the fact that every quotient map onto c₀ is completely continuous. Other weak sequential continuity results on polynomials and analytic mappings related to the (DP*) property are shown.

Some results on the class of σ -unbounded Dunford-Pettis operators

Noufissa Hafidi, Jawad H'michane (2021)

Commentationes Mathematicae Universitatis Carolinae

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We introduce and study the class of unbounded Dunford--Pettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.

A note on L-Dunford-Pettis sets in a topological dual Banach space

Abderrahman Retbi (2020)

Czechoslovak Mathematical Journal

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The present paper is devoted to some applications of the notion of L-Dunford-Pettis sets to several classes of operators on Banach lattices. More precisely, we establish some characterizations of weak Dunford-Pettis, Dunford-Pettis completely continuous, and weak almost Dunford-Pettis operators. Next, we study the relationships between L-Dunford-Pettis, and Dunford-Pettis (relatively compact) sets in topological dual Banach spaces.

Weakly precompact subsets of L₁(μ,X)

Ioana Ghenciu (2012)

Colloquium Mathematicae

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Let (Ω,Σ,μ) be a probability space, X a Banach space, and L₁(μ,X) the Banach space of Bochner integrable functions f:Ω → X. Let W = f ∈ L₁(μ,X): for a.e. ω ∈ Ω, ||f(ω)|| ≤ 1. In this paper we characterize the weakly precompact subsets of L₁(μ,X). We prove that a bounded subset A of L₁(μ,X) is weakly precompact if and only if A is uniformly integrable and for any sequence (fₙ) in A, there exists a sequence (gₙ) with g ₙ ∈ c o f i : i ≥ n for each n such that for a.e. ω ∈ Ω, the sequence (gₙ(ω)) is weakly...

On projectional skeletons in Vašák spaces

Ondřej F. K. Kalenda (2017)

Commentationes Mathematicae Universitatis Carolinae

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We provide an alternative proof of the theorem saying that any Vašák (or, weakly countably determined) Banach space admits a full 1 -projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W. Kubiś (2009) in case of weakly compactly generated spaces.

On Pettis integrability

Juan Carlos Ferrando (2003)

Czechoslovak Mathematical Journal

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Assuming that ( Ω , Σ , μ ) is a complete probability space and X a Banach space, in this paper we investigate the problem of the X -inheritance of certain copies of c 0 or ℓ ∞ in the linear space of all [classes of] X -valued μ -weakly measurable Pettis integrable functions equipped with the usual semivariation norm.