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Jones Index Theory for C*-Algebras

  • Yasuo Watatani
Part of the Progress in Mathematics book series (PM, volume 84)

Abstract

The notion of index [M : N] was introduced by Jones [13] as an invariant for subfactors N of a factor M of type II1. Subsequently Kosaki [18] defined an index E for a conditional expectation E of an arbitrary factor M onto a subfactor N using the spatial theory of Connes [6] and the theory of operator-valued weights of Haagerup [9]. We shall define an index E for a conditional expectation E on a C*-algebra. This index theory for C*-algebras is a mixture of the index theory by Jones and the theory of Morita equivalence by Rieffel [24], [25]. We establish the link between transfer in K -theory and a multiplication by Index E.

Keywords

Conditional Expectation Operator Algebra Index Theory Basic Construction Irrational Rotation 
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 Science+Business Media New York 1991

Authors and Affiliations

  • Yasuo Watatani
    • 1
  1. 1.Osaka Kyoiku UniversityTennoji, OsakaJapan

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