Descent of Hilbert *-modules

  • Tyrone Crisp

    Radboud University Nijmegen, The Netherlands, and University of Maine, Orono, USA
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Let be a right Hilbert *-module over a *-algebra , and suppose that is equipped with a left action, by compact operators, of a second *-algebra . Tensor product with gives a functor from Hilbert *-modules over to Hilbert *-modules over . We prove that under certain conditions (which are always satisfied if, for instance, is nuclear), the image of this functor can be described in terms of coactions of a certain coalgebra canonically associated to . We then discuss several examples that fit into this framework: parabolic induction of tempered group representations; Hermitian connections on Hilbert *-modules; Fourier (co)algebras of compact groups; and the maximal *-dilation of operator modules over non-self-adjoint operator algebras.

Cite this article

Tyrone Crisp, Descent of Hilbert *-modules. J. Noncommut. Geom. 14 (2020), no. 2, pp. 487–529

DOI 10.4171/JNCG/371