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

Entropy 

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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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