Dunford-Pettis-like properties of projective and natural tensor product spaces.

Jesús M. Fernández Castillo; Juan A. López Molina

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Displaying similar documents to “Dunford-Pettis-like properties of projective and natural tensor product spaces.”

On Banach spaces X such that L(Lp,X) = K(Lp,X).

Jesús M. Martínez Castillo (1995)

Extracta Mathematicae

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Absolutely (∞,p) summing and weakly-p-compact operators in Banach spaces.

Jesús M. Fernández Castillo (1990)

Extracta Mathematicae

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A sequence (x) in a Banach space X is said to be weakly-p-summable, 1 ≤ p < ∞, when for each x* ∈ X*, (x*x) ∈ l. We shall say that a sequence (x) is weakly-p-convergent if for some x ∈ X, (x - x) is weakly-p-summable.

Non-containment of l in projective tensor products of Banach spaces.

J. C. Díaz Alcaide (1990)

Revista Matemática de la Universidad Complutense de Madrid

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Two properties on projective tensor products are introduced and briefly studied. We apply them to give sufficient conditions to assure the non-containment of l1 in a projective tensor product of Banach spaces.

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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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.

Absolutely (∞,p) summing and weakly-p-compact operators in C(K).

Jesús M. Fernández Castillo (1990)

Extracta Mathematicae

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In this note we review some results about: 1. Representation of Absolutely (∞,p) summing operators (∏_∞,p) in C(K,E) 2. Dunford-Pettis properties.

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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About certain isomorphic properties of Banach spaces in projective tensor products.

Giovanni Emmanuele (1990)

Extracta Mathematicae

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This note is an announcement of results contained in the papers [4], [5], [6] concerning isomorphic properties of Banach spaces in projective tensor products (for this definition and some property we refer to [1]). At the end, some new result is obtained too.

Unconditionally p-null sequences and unconditionally p-compact operators

Ju Myung Kim (2014)

Studia Mathematica

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We investigate sequences and operators via the unconditionally p-summable sequences. We characterize the unconditionally p-null sequences in terms of a certain tensor product and then prove that, for every 1 ≤ p < ∞, a subset of a Banach space is relatively unconditionally p-compact if and only if it is contained in the closed convex hull of an unconditionally p-null sequence.

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|, ...