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On the three-space problem for the Dunford-Pettis property

Published online by Cambridge University Press:  17 April 2009

J.M.F. Castillo  and
M.A. Simoes
J.M.F. Castillo
Affiliation:
Departamento de MatemáticasUniversidad de ExtremaduraAvenida de Elvas06071-BadajozSpain e-mail: castillo@unex.es
M.A. Simoes
Affiliation:
Dipartimento di MatematicaUniversitá di Roma I“La Sapienza”, Piazzale Aldo Moro 2I-00185 RomaItaly, e-mail: simoes@mat.uniroma1.it
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A Banach space X is called a twisted sum of the Banach spaces Y and Z if it has a subspace isomorphic to Y in such a way that the corresponding quotient is isomorphic to Z. In this paper we study twisted sums of Banach spaces with either have the Dunford-Pettis property, are c0-saturated or l1-saturated. Amongst other things, we show that every Banach space is a complemented subspace of a twisted sum of two Banach spaces with the Dunford-Pettis property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 487 - 493
Copyright
Copyright © Australian Mathematical Society 1999

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