2017/10/19 by Tyrone Crisp, Crisp, Tyrone
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1710.07130
37 pages. Fixed a typo in the definition of curvature in Definition 6.9
arxiv created 2020/06/17 · arxiv updated 2020/06/19
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.