Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Frobenius reciprocity and the Haagerup tensor product


Author: Tyrone Crisp
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 46M15; Secondary 22D30, 46L07
DOI: https://doi.org/10.1090/tran/7203
Published electronically: May 30, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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 functor of unitary induction for a closed subgroup $ H$ of a locally compact group $ G$ admits a left adjoint in this setting if and only if $ H$ is cocompact in $ G$. The adjoint functor is given by the Haagerup tensor product with the operator-theoretic adjoint of Rieffel's induction bimodule.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 46M15, 22D30, 46L07

Retrieve articles in all journals with MSC (2010): 46M15, 22D30, 46L07


Additional Information

Tyrone Crisp
Affiliation: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
Address at time of publication: Department of Mathematics, Radboud University Nijmegen, P.O. Box 9010, 6500GL Nijmegen, The Netherlands
Email: t.crisp@math.ru.nl

DOI: https://doi.org/10.1090/tran/7203
Received by editor(s): October 18, 2016
Received by editor(s) in revised form: February 3, 2017
Published electronically: May 30, 2018
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society