Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Crossed products of Hilbert $C^*$-modules


Author: Huu Hung Bui
Journal: Proc. Amer. Math. Soc. 125 (1997), 1341-1348
MSC (1991): Primary 46L05, 22D25
DOI: https://doi.org/10.1090/S0002-9939-97-03656-3
MathSciNet review: 1363451
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We define the notion of crossed products of Hilbert $C^*$-modules by regular multiplicative unitaries, which is a generalization of the notion of crossed products of $C^*$-algebras. Crossed products of Hilbert $C^*$-modules arise naturally as imprimitivity bimodules for the crossed products of Morita equivalent $C^*$-algebras.


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

  • [Bl] B. Blackadar, K-Theory for operator algebras, Math. Sci. Research Institute Publications 5, Springer-Verlag, New York-Berlin-Heidelberg, 1986. MR 88g:46082
  • [B] H. H. Bui, Morita equivalence of twisted crossed products by coactions, J. Funct. Anal., 123(1994), 59-98. MR 95g:46121
  • [B2] H. H. Bui, Full coactions on Hilbert $C^{*}$-modules, J. Austral. Math. Soc. (Series A), 59(1995), 409-420. MR 96j:46067
  • [BS] S. Baaj and G. Skandalis, $C^{*}$-algèbres de Hopf et théorie de Kasparov équivariante, K-theory 2(1989), 683-721. MR 90j:46061
  • [BS2] S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualite pour les produits crosés de $C^{*}$-algèbres, Ann. Sci. Ec. Norm. Sup. 26(1993), 425-488. MR 94e:46127
  • [DW] R. S. Doran and J. Wichmann, Approximate identities and factorization in Banach modules, Lecture Notes in Mathematics, Vol. 768, Springer-Verlag, Berlin-Heidelberg-New York, 1979. MR 83e:46044
  • [ER] S. Echterhoff and I. Raeburn, Multipliers of imprimitivity bimodules and Morita equivalence of crossed products, Math. Scand., 76(1995), 289-309. CMP 96:02
  • [L] E. C. Lance, Hilbert $C^{*}$-modules, London Math. Soc., Lecture Note Series 210, 1995. MR 96k:46100
  • [LPRS] M. B. Landstad, J. Phillips, I. Raeburn and C. E. Sutherland, Representations of crossed products by coactions and principal bundles, Trans. Amer. Math. Soc. 299(1987), 747-784. MR 88f:46127
  • [S] S. Sakai, $C^{*}$-algebras and $W^{*}$-algebras, Ergebnisse der Mathmatik, Band 60, Springer-Verlag, New York-Heidelberg-Berlin, 1971. MR 56:1082
  • [W] S. L. Woronowicz, Unbounded elements affiliated with $C^{*}$-algebras and non-compact quantum groups, Commun. Math. Phys., 136(1991),399-432. MR 92b:46117

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L05, 22D25

Retrieve articles in all journals with MSC (1991): 46L05, 22D25


Additional Information

Huu Hung Bui
Affiliation: School of Mathematics, Physics, Computing and Electronics, Macquarie University, New South Wales 2109, Australia
Address at time of publication: School of Mathematics, University of New South Wales, Sydney 2052, New South Wales, Australia
Email: hung@macadam.mpce.mq.edu.au, hung@alpha.maths.unsw.edu.au

DOI: https://doi.org/10.1090/S0002-9939-97-03656-3
Received by editor(s): August 4, 1995
Received by editor(s) in revised form: October 6, 1995, October 12, 1995, and October 30, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society