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On the reciprocal Dunford-Pettis property in projective tensor products

  • G. Emmanuele (a1)

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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