ABSTRACT. In this paper we introduce the notion of Hubert C*-bimodules, replacing the associativity condition of two-sided inner products in Rieffel's imprimitivity bimodulcs by a Pimsner-Popa type inequality. We prove Schur's Lemma and Frobenius reciprocity in this setting. We define minimality of Hubert C*-bimodules and show that tensor products of minimal bimodules are also minimal. For an A-A bimodule which is compatible with a trace on a unital C*-algebra A, its dimension (square root of Jones index) depends only on its KK-class. Finally, we show that the dimension map transforms the Kasparov products in KK(A, A) to the product of positive real numbers, and determine the subring of KK(A, A) generated by the Hubert C*-bimodules for a C*-algebra generated by Jones projections.
|Number of pages||44|
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 2000|
- Hubert c*-bimodule
- Jones index
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