Displaying similar documents to “A note on L-Dunford-Pettis sets in a topological dual Banach space”

Quantification of the reciprocal Dunford-Pettis property

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

Studia Mathematica

Similarity:

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.

Almost Weakly Compact Operators

Ioana Ghenciu, Paul Lewis (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

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.

The weak compactness of almost Dunford-Pettis operators

Belmesnaoui Aqzzouz, Aziz Elbour, Othman Aboutafail (2011)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.

An approach to Schreier's space.

Jesús M. Fernández Castillo, Manuel González (1991)

Extracta Mathematicae

Similarity:

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 |xj|, ...

On certain subsets of Bochner integrable function spaces.

Fernando Bombal (1991)

Extracta Mathematicae

Similarity:

One of the most important methods used in literature to introduce new properties in a Banach space E, consists in establishing some non trivial relationships between different classes of subsets of E. For instance, E is reflexive, or has finite dimension, if and only if every bounded subset is weakly relatively compact or norm relatively compact, respectively. On the other hand, Banach spaces of the type C(K) and Lp(μ) play a vital role in the general...