Annals of Functional Analysis

Green’s theorem for crossed products by Hilbert C-bimodules

Mauricio Achigar

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Green’s theorem gives a Morita equivalence C0(G/H,A)GAH for a closed subgroup H of a locally compact group G acting on a C-algebra A. We prove an analogue of Green’s theorem in the case G=Z, where the automorphism generating the action is replaced by a Hilbert C-bimodule.

Article information

Ann. Funct. Anal., Volume 8, Number 3 (2017), 281-290.

Received: 23 April 2016
Accepted: 26 September 2016
First available in Project Euclid: 4 April 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L08: $C^*$-modules
Secondary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20] 46L05: General theory of $C^*$-algebras

Green’s theorem Morita equivalence crossed product Hilbert module


Achigar, Mauricio. Green’s theorem for crossed products by Hilbert $C^{*}$ -bimodules. Ann. Funct. Anal. 8 (2017), no. 3, 281--290. doi:10.1215/20088752-0000013X.

Export citation


  • [1] B. Abadie and M. Achigar, Cuntz-Pimsner $C^{*}$-algebras and crossed products by Hilbert $C^{*}$-bimodules, Rocky Mountain J. Math. 39 (2009), no. 4, 1051–1081.
  • [2] B. Abadie, S. Eilers, and R. Exel, Morita equivalence for crossed products by Hilbert $C^{*}$-bimodules, Trans. Amer. Math. Soc. 350 (1998), no. 8, 3043–3054.
  • [3] E. C. Lance, Hilbert $C^{*}$-Modules: A Toolkit for Operator Algebraists, London Math. Soc. Lecture Note Ser. 210, Cambridge Univ. Press, Cambridge, 1995.
  • [4] M. V. Pimsner, “A class of $C^{*}$-algebras generalizing both Cuntz-Krieger algebras and crossed products by $\mathbb{Z}$” in Free Probability Theory (Waterloo, 1995), Fields Inst. Commun. 12, Amer. Math. Soc., Providence, 1997, 189–212.
  • [5] D. P. Williams, Crossed Products of $C^{*}$-Algebras, Math. Surveys Monogr. 134, Amer. Math. Soc., Providence, 2007.