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The Dunford–Pettis property on tensor products

Published online by Cambridge University Press:  26 October 2001

MANUEL GONZÁLEZ  and
JOAQUÍN M. GUTIÉRREZ
MANUEL GONZÁLEZ
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain; e-mail: gonzalem@ccaix3.unican.es
JOAQUÍN M. GUTIÉRREZ
Affiliation:
Departamento de Matemática Aplicada, ETS de Ingenieros Industriales Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain; e-mail: jgutierrez@etsii.upm.es
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Abstract

We show that, in some cases, the projective and the injective tensor products of two Banach spaces do not have the Dunford–Pettis property (DPP). As a consequence, we obtain that (c0 &[otimes ]circ;πc0)** fails the DPP. Since (c0 &[otimes ]circ;πc0)* does enjoy it, this provides a new space with the DPP whose dual fails to have it. We also prove that, if E and F are [Lscr ]1-spaces, then E &[otimes ]circ;ε has the DPP if and only if both E and F have the Schur property. Other results and examples are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 1 , July 2001 , pp. 185 - 192
Copyright
2001 Cambridge Philosophical Society

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