### On some subsets of ${L}_{1}(\mu ,E)$

Fernando Bombal (1991)

Czechoslovak Mathematical Journal

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Fernando Bombal (1991)

Czechoslovak Mathematical Journal

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Fernando Bombal (1990)

Extracta Mathematicae

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Fernando Bombal, Pilar Cembranos, José Mendoza (1989)

Extracta Mathematicae

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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}|,
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Fernando Bombal Gordon (1986)

Extracta Mathematicae

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Michael A. Coco (2004)

Studia Mathematica

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We give biorthogonal system characterizations of Banach spaces that fail the Dunford-Pettis property, contain an isomorphic copy of c₀, or fail the hereditary Dunford-Pettis property. We combine this with previous results to show that each infinite-dimensional Banach space has one of three types of biorthogonal systems.

Giovanni Emmanuele (1988)

Extracta Mathematicae

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Jesús M. Fernández Castillo (1992)

Extracta Mathematicae

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