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Fréchet AL-spaces have the Dunford-Pettis property

Published online by Cambridge University Press:  17 April 2009

J.C. Díaz ,
A. Fernández  and
F. Naranjo
J.C. Díaz
Affiliation:
Dpto. Matemáticas, E.T.S.I.A.M., Universidad de Córdoba, 14004 - Córdoba, Spain e-mail: [email protected]
A. Fernández
Affiliation:
Dpto. Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos s/n, 41092 - Sevilla, Spain e-mail: [email protected]
F. Naranjo
Affiliation:
Dpto. Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos s/n, 41092 – Sevilla, Spain
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Abstract

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A Fréchet lattice E is an AL-space if its topology can be defined by a family of lattice seminorms that are additive in the positive cone of E. Grothendieck proved that AL-Banach spaces have the Dunford-Pettis property. This result was recently extended by Fernández and Naranjo to AL-Fréchet spaces with a continuous norm and weak order unit. In this note we show how to remove both hypotheses.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 383 - 386
Copyright
Copyright © Australian Mathematical Society 1998

References

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