Jones Index Theory for C*-Algebras
The notion of index [M : N] was introduced by Jones  as an invariant for subfactors N of a factor M of type II1. Subsequently Kosaki  defined an index E for a conditional expectation E of an arbitrary factor M onto a subfactor N using the spatial theory of Connes  and the theory of operator-valued weights of Haagerup . 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 , . We establish the link between transfer in K -theory and a multiplication by Index E.
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