The Dunford-Pettis property in C*-algebras
Cho-Ho Chu, Bruno Iochum (1990)
Studia Mathematica
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Displaying similar documents to “The alternative Dunford-Pettis Property in the predual of a von Neumann algebra”
The Dunford-Pettis property in C*-algebras
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 -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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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.
On the Dunford-Pettis property
Bombal, Fernando (1988)
Portugaliae mathematica
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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.
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 the Dunford-Pettis property for quotients of C(K) spaces, K dispersed.
Ricardo García (1995)
Extracta Mathematicae
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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...
On weakly closed functions
N. Ergun, T. Noiri (1990)
Matematički Vesnik
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A problem of von Neumann and Maharam about algebras supporting continuous submeasures
Stevo Todorcevic (2004)
Fundamenta Mathematicae
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We show that a σ-algebra 𝔹 carries a strictly positive continuous submeasure if and only if 𝔹 is weakly distributive and it satisfies the σ-finite chain condition of Horn and Tarski.
On the equality between some classes of operators on Banach lattices
Belmesnaoui Aqzzouz, Aziz Elbour, Mohammed Moussa (2012)
Mathematica Bohemica
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We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.