Israel Journal of Mathematics

, Volume 199, Issue 2, pp 641–650 | Cite as

Topological freeness for Hilbert bimodules

  • Bartosz Kosma KwaśniewskiEmail author


It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A X ℤ. An ideal lattice description and a simplicity criterion for A X ℤ are established.


Irreducible Representation American Mathematical Society Faithful Representation Covariant Representation Topological Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. Abadie, S. Eilers and R. Exel, Morita equivalence for crossed products by Hilbert C*-bimodules, Transactions of the American Mathematical Society 350 (1998), 3043–3054.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    A. B. Antonevich and A. V. Lebedev, Functional Differential Equations: I. C*-theory, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 70, Longman Scientific & Technical, Harlow, 1994.Google Scholar
  3. [3]
    R. J. Archbold and J. S. Spielberg, Topologically free actions and ideals in discrete C*-dynamical systems, Proceedings of the Edinburgh Mathematical Society 37 (1993), 119–124.CrossRefMathSciNetGoogle Scholar
  4. [4]
    S. Boyd, N. Keswani and I. Raeburn, Faithful representations of crossed products by endomorphisms, Proceedings of the American Mathematical Society 118 (1993), 427–436.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    L. G. Brown, J. Mingo and N. Shen, Quasi-multipliers and embeddings of hilbert C*-modules, Canadian Journal of Mathematics 71 (1994), 1150–1174.CrossRefMathSciNetGoogle Scholar
  6. [6]
    S. Doplicher and J. E. Roberts, Duals of compact lie groups realized in the Cuntz algebras and their actions on C*-algebras, Journal of Functional Analysis 74 (1987), 96–120.CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    G. A. Elliot, Some simple C*-algebras constructed as crossed products with discrete outer automorphism groups, Kyoto University. Research Institute for Mathematical Sciences. Publications 13 (1980), 299–311.CrossRefGoogle Scholar
  8. [8]
    R. Exel, M. Laca and J. Quigg, Partial dynamical systems and C*-algebras generated by partial isometries, Journal of Operator Theory 47 (2002), 169–186.zbMATHMathSciNetGoogle Scholar
  9. [9]
    T. Katsura, Ideal structure of C*-algebras associated with C*-correspondences, Pacific Journal of Mathematics 230 (2007), 107–146.CrossRefzbMATHMathSciNetGoogle Scholar
  10. [10]
    S. Kawamura and J. Tomiyama, Properties of topological dynamical systems and corresponding C*-algebras, Tokyo Journal of Mathematics 13 (1990), 251–257.CrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    B. K. Kwaśniewski, C*-algebras generalizing both relative Cuntz-Pimsner and Doplicher-Roberts algebras, Transactions of the American Mathematical Society 365 (2013), 1809–1873.CrossRefzbMATHMathSciNetGoogle Scholar
  12. [12]
    A. V. Lebedev, Topologically free partial actions and faithful representations of partial crossed products, Functional Analysis and its Applications 39 (2005), 207–214.CrossRefzbMATHMathSciNetGoogle Scholar
  13. [13]
    P. S. Muhly and B. Solel, Tensor algebras over C*-correspondences (representations, dilations, and C*-envelopes), Journal of Functional Analysis 158 (1998), 389–457.CrossRefzbMATHMathSciNetGoogle Scholar
  14. [14]
    D. P. O’Donovan, Weighted shifts and covariance algebras, Transactions of the American Mathematical Society 208 (1975), 1–25.CrossRefzbMATHMathSciNetGoogle Scholar
  15. [15]
    D. Olesen and G. K. Pedersen, Applications of the Connes spectrum to C*-dynamical systems, Journal of Functional Analysis 30 (1978), 179–197.CrossRefzbMATHMathSciNetGoogle Scholar
  16. [16]
    I. Raeburn and D. P. Williams, Morita Equivalence and Continuous-Trace C*-Algebras, Mathematical Surveys and Monographs, Vol. 60, American Mathematical Society, Providence, RI, 1998.CrossRefzbMATHGoogle Scholar

Copyright information

© Hebrew University Magnes Press 2014

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of BialystokBialystokPoland

Personalised recommendations