Operator Ideals

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


In this chapter we study the spaces of bilinear forms and operators that can be generated from a tensor norm. For each tensor norm α, we have the α-integral and the α-nuclear forms or operators. We introduce the concept of a Banach operator ideal and we develop just enough of the theory to explain the relationship between tensor norms and operator ideals. In particular, we see that the α-integral and α-nuclear classes constitute the maximal and minimal ideals respectively.


Banach Space Bilinear Form Operator Ideal Approximation Property Finite Dimensional Space 
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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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