The Approximation Property

  • Raymond A. Ryan
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter we introduce the approximation property for Banach spaces. The possession of this property leads to the resolution of several outstanding issues concerning projective and injective tensor products. We then consider the following question: when are the projective or injective tensor products of reflexive spaces themselves reflexive? A satisfactory answer requires the use of the approximation property. Finally, we study tensor products of Banach spaces with Schauder bases.


Banach Space Tensor Product Compact Subset Compact Operator Approximation Property 
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Copyright information

© Springer-Verlag London 2002

Authors and Affiliations

  • Raymond A. Ryan
    • 1
  1. 1.Department of MathematicsNational University of Ireland, GalwayGalwayIreland

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