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Operator Ideals

  • Raymond A. Ryan
Chapter
  • 1.1k Downloads
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

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.

Keywords

Banach Space Bilinear Form Operator Ideal Approximation Property Finite Dimensional Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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