Skip to main content
×
Home
    • Aa
    • Aa

On the reciprocal Dunford-Pettis property in projective tensor products

  • G. Emmanuele (a1)
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*).

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 1 *
Loading metrics...

Abstract views

Total abstract views: 30 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 29th May 2017. This data will be updated every 24 hours.