Geodesic
Quasi-Multipliers and Embeddings of Hilbert C*-Bimodules
Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1150-1174

Voir la notice de l'article provenant de la source Cambridge University Press

This paper considers Hilbert C*-bimodules, a slight generalization of imprimitivity bimodules which were introduced by Rieffel [20]. Brown, Green, and Rieffel [7] showed that every imprimitivity bimodule X can be embedded into a certain C*-algebra L, called the linking algebra of X. We consider arbitrary embeddings of Hilbert C*-bimodules into C*-algebras; i.e. we describe the relative position of two arbitrary hereditary C*-algebras of a C*-algebra, in an analogy with Dixmier's description [10] of the relative position of two subspaces of a Hilbert space.The main result of this paper (Theorem 4.3) is taken from the doctoral dissertation of the third author [22], although the proof here follows a different approach. In Section 1 we set out the definitions and basic properties (mostly folklore) of Hilbert C*-bimodules. In Section 2 we show how every quasi-multiplier gives rise to an embedding of a bimodule. In Section 3 we show that , the enveloping C*-algebra of the C*-algebraA with its product perturbed by a positive quasi-multiplier , is isomorphic to the closure (Proposition 3.1). Section 4 contains the main theorem (4.3), and in Section 5 we explain the analogy with the relative position of two subspaces of a Hilbert spaces and present some complements. 
Brown, Lawrence G.; Mingo, James A.; Shen, Nien-Tsu. Quasi-Multipliers and Embeddings of Hilbert C*-Bimodules. Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1150-1174. doi: 10.4153/CJM-1994-065-5
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