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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 131, Issue 1
  • July 2001, pp. 185-192

The Dunford–Pettis property on tensor products

  • MANUEL GONZÁLEZ (a1) and JOAQUÍN M. GUTIÉRREZ (a2)
  • DOI: http://dx.doi.org/10.1017/S0305004101005175
  • Published online: 26 October 2001
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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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