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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Emmanuele, G. 2014. On complemented copies of c 0 and ℓ ∞. Acta Mathematica Hungarica, Vol. 142, Issue. 2, p. 348.


    Salimi, M. and Moshtaghioun, S. M. 2012. A New Class of Banach Spaces and Its Relation with Some Geometric Properties of Banach Spaces. Abstract and Applied Analysis, Vol. 2012, p. 1.


    Bunce, Leslie J. and Peralta, Antonio M. 2007. Dunford–Pettis properties, Hilbert spaces and projective tensor products. Journal of Functional Analysis, Vol. 253, Issue. 2, p. 692.


    Gonzalez, Manuel 1994. On essentially incomparable Banach spaces. Mathematische Zeitschrift, Vol. 215, Issue. 1, p. 621.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 109, Issue 1
  • January 1991, pp. 161-166

On the reciprocal Dunford-Pettis property in projective tensor products

  • G. Emmanuele (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100069632
  • Published online: 24 October 2008
Abstract
Abstract

We prove the following result: if a Banach space E does not contain l1 and F has the (RDPP), then EnF has the same property, provided that L(E, F*) = K(E, F*). Hence we prove that if En F has the (RDPP) then at least one of the spaces E and F must not contain l1. Some corollaries are then presented as well as results concerning the necessity of the hypothesis L(E, F*) = K(E, F*).

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[8]A. Grothendieck . Sur les applicationes lineaires faiblement compactes d'éspace du type C(K). Canad. J. Math. 5 (1953), 129173.

[9]N. J. Kalton , E. Saab and P. Saab . On the Dieudonné property for C(Ω,E). Proc. Amer. Math. Soc. 96 (1986), 5052.

[11]D. R. Lewis . Conditional weak compactness in certain inductive tensor products. Math. Ann. 201 (1973), 201209.

[14]G. Pisier , Factorization of Linear Operators and Geometry of Banach Spaces. CBMS Regional Conf. Series in Math. no. 60 (American Mathematical Society, 1986).

[16]L. Tzafriri . Reflexivity in Banach lattices and their subspaces. J. Funct. Anal. 10 (1972), 118.

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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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