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.
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Watatani, Y. (1991). Jones Index Theory for C*-Algebras. In: Araki, H., Kadison, R.V. (eds) Mappings of Operator Algebras. Progress in Mathematics, vol 84. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0453-4_13
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DOI: https://doi.org/10.1007/978-1-4612-0453-4_13
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