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Displaying similar documents to “Absolutely (∞,p) summing and weakly-p-compact operators in C(K).”

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 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.

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

Jesús M. Fernández Castillo, Juan A. López Molina (1993)

Revista Matemática de la Universidad Complutense de Madrid

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Several properties of weakly p-summable sequences and of the scale of p-converging operators (i.e., operators transforming weakly p-summable sequences into convergent sequences) in projective and natural tensor products with an lp space are considered. The last section studies the Dunford-Pettis property of order p (i.e., every weakly compact operator is p-convergent) in those spaces.

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.