The Dunford-Pettis property in C*-algebras

Cho-Ho Chu; Bruno Iochum

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Displaying similar documents to “The Dunford-Pettis property in C*-algebras”

The alternative Dunford-Pettis Property in the predual of a von Neumann algebra

Miguel Martín, Antonio M. Peralta (2001)

Studia Mathematica

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Let A be a type II von Neumann algebra with predual A⁎. We prove that A⁎ does not have the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (φₙ) converging weakly to φ in A⁎ with ||φₙ|| = ||φ|| = 1 for all n ∈ ℕ and a weakly null sequence (xₙ) in A such that φₙ(xₙ) ↛ 0. This answers a question posed in [7].

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.

A new operator characterization of the Dunford-Pettis property

Fernando Bombal Gordon (1987)

Extracta Mathematicae

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On the Dunford-Pettis property

Bombal, Fernando (1988)

Portugaliae mathematica

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A note on the Dunford-Pettis property for quotients of C(K) spaces, K dispersed.

Ricardo García (1995)

Extracta Mathematicae

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The Dunford-Pettis property, the Gelfand-Phillips property, and L-sets

Ioana Ghenciu, Paul Lewis (2006)

Colloquium Mathematicae

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The Dunford-Pettis property and the Gelfand-Phillips property are studied in the context of spaces of operators. The idea of L-sets is used to give a dual characterization of the Dunford-Pettis property.

Almost Weakly Compact Operators

Ioana Ghenciu, Paul Lewis (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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Dunford-Pettis type properties are studied in individual Banach spaces as well as in spaces of operators. Bibasic sequences are used to characterize Banach spaces which fail to have the Dunford-Pettis property. The question of whether a space of operators has a Dunford-Pettis property when the dual of the domain and the codomain have the respective property is studied. The notion of an almost weakly compact operator plays a consistent and important role in this study.

Quantification of the reciprocal Dunford-Pettis property

Ondřej F. K. Kalenda, Jiří Spurný (2012)

Studia Mathematica

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We prove in particular that Banach spaces of the form C₀(Ω), where Ω is a locally compact space, enjoy a quantitative version of the reciprocal Dunford-Pettis property.

Dunford-Pettis-like properties of continuous vector function spaces.

Jesús M. Fernández Castillo, Fernando Sánchez (1993)

Revista Matemática de la Universidad Complutense de Madrid

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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...

A new proof that every weakly compact operator with domain L(μ) is representable.

Diómedes Bárcenas (1991)

Extracta Mathematicae

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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.

An approach to Schreier's space.

Jesús M. Fernández Castillo, Manuel González (1991)

Extracta Mathematicae

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In 1930, J. Schreier [10] introduced the notion of admissibility in order to show that the now called weak-Banach-Saks property does not hold in every Banach space. A variation of this idea produced the Schreier's space (see [1],[2]). This is the space obtained by completion of the space of finite sequences with respect to the following norm: ||x||_S = sup_{(A admissible)} ∑_{j ∈ A} |x_j|, ...