Descent of Hilbert C*-modules
Abstract
Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert C*-modules over B. We prove that under certain conditions (which are always satisfied if, for instance, A is nuclear), the image of this functor can be described in terms of coactions of a certain coalgebra canonically associated to F. We then discuss several examples that fit into this framework: parabolic induction of tempered group representations; Hermitian connections on Hilbert C*-modules; Fourier (co)algebras of compact groups; and the maximal C*-dilation of operator modules over non-self-adjoint operator algebras.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2017
- DOI:
- 10.48550/arXiv.1710.07130
- arXiv:
- arXiv:1710.07130
- Bibcode:
- 2017arXiv171007130C
- Keywords:
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- Mathematics - Operator Algebras
- E-Print:
- 37 pages. Fixed a typo in the definition of curvature in Definition 6.9