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Frobenius reciprocity and the Haagerup tensor product
2018
Transactions of the American Mathematical Society
In the context of operator-space modules over C * -algebras, we give a complete characterisation of those C * -correspondences whose associated Haagerup tensor product functors admit left adjoints. The characterisation, which builds on previous joint work with N. Higson, exhibits a close connection between the notions of adjoint operators and adjoint functors. As an application, we prove a Frobenius reciprocity theorem for representations of locally compact groups on operator spaces: the
doi:10.1090/tran/7203
fatcat:uaud5ylh3zawrghdh326tjkg44