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Countably generated Hilbert modules, the Kasparov Stabilisation Theorem, and frames in Hilbert modules


Authors: Iain Raeburn and Shaun J. Thompson
Journal: Proc. Amer. Math. Soc. 131 (2003), 1557-1564
MSC (2000): Primary 46L08
DOI: https://doi.org/10.1090/S0002-9939-02-06787-4
Published electronically: October 1, 2002
MathSciNet review: 1949886
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Abstract: We consider a class of countably generated Hilbert modules in which the generators are multipliers of the module, and prove a version of the Kasparov Stabilisation Theorem for these modules. We then extend recent work of Frank and Larson on frames in Hilbert modules.


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

  • 1. S. Baaj and G. Skandalis, $C^*$-algèbres de Hopf et théorie de Kasparov équivariante, $K$-Theory 2 (1989), 683-721. MR 90j:46061
  • 2. B. Blackadar, article to appear in the Encyclopedia of Mathematics.
  • 3. L.G. Brown, P. Green and M.A. Rieffel, Stable isomorphism and strong Morita equivalence of $C^*$-algebras, Pacific J. Math. 71 (1977), 349-363. MR 57:3866
  • 4. S. Echterhoff and I. Raeburn, Multipliers of imprimitivity bimodules and Morita equivalence of crossed products, Math. Scand. 76 (1995), 289-309. MR 97h:46093
  • 5. M. Frank and D.R. Larson, Frames in Hilbert $C^*$-modules and $C^*$-algebras, J. Operator Theory, to appear.
  • 6. M. Frank and D.R. Larson, A module frame concept for Hilbert $C^*$-modules, The Functional and Harmonic Analysis of Wavelets and Frames, Contemp. Math. vol. 247, Amer. Math. Soc., Providence, 1999, pages 207-233. MR 2001b:46094
  • 7. K.K. Jensen and K. Thomsen, Elements of $KK$-Theory, Birkhäuser, Boston, 1991. MR 94b:19008
  • 8. E.C. Lance, Hilbert $C^*$-Modules: A Toolkit for Operator Algebraists, London Math. Soc. Lecture Note Series, vol. 210, Cambridge Univ. Press, 1994.
  • 9. J.A. Mingo and W.J. Phillips, Equivariant triviality theorems for Hilbert $C^*$-modules, Proc. Amer. Math. Soc. 91 (1984), 225-230. MR 85f:46111
  • 10. I. Raeburn and D.P. Williams, Morita Equivalence and Continuous-Trace $C^*$-Algebras, Math. Surveys and Monographs, vol. 60, Amer. Math. Soc., Providence, 1998. MR 2000c:46108

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Additional Information

Iain Raeburn
Affiliation: Department of Mathematics, University of Newcastle, New South Wales 2308, Australia
Email: iain@frey.newcastle.edu.au

Shaun J. Thompson
Affiliation: Department of Mathematics, University of Newcastle, New South Wales 2308, Australia
Email: shaun@frey.newcastle.edu.au

DOI: https://doi.org/10.1090/S0002-9939-02-06787-4
Received by editor(s): February 16, 2001
Received by editor(s) in revised form: January 3, 2002
Published electronically: October 1, 2002
Additional Notes: This research was supported by the Australian Research Council.
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society

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