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Tietze extension theorem for Hilbert $C^*$-modules


Author: Damir Bakic
Journal: Proc. Amer. Math. Soc. 133 (2005), 441-448
MSC (2000): Primary 46C50; Secondary 46L08
DOI: https://doi.org/10.1090/S0002-9939-04-07563-X
Published electronically: August 25, 2004
MathSciNet review: 2093066
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Abstract: We prove the following generalization of the noncommutative Tietze extension theorem: if $V$ is a countably generated Hilbert $C^*$-module over a $\sigma$-unital $C^*$-algebra, then the canonical extension $\overline{\Phi}$ of a surjective morphism $\Phi : V \rightarrow W$ of Hilbert $C^*$-modules to extended (multiplier) modules, $\overline{\Phi} : V_d \rightarrow W_d$, is also surjective.


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

  • 1. D. Bakic, B. Guljas, On a class of module maps of Hilbert $C^*$-modules, Mathematical Communications 7(2002) No.2, 177-192. MR 1952758 (2003k:46084)
  • 2. D. Bakic, B. Guljas, Extensions of Hilbert $C^*$-modules, to appear in Houston J. Math.
  • 3. L. G. Brown, P. Green, M. A. Rieffel, Stable isomorphism and strong Morita equivalence of $C^*$-algebras, Pacific J. Math, 71(1977), 349-363. MR 0463928 (57:3866)
  • 4. X. Fang, The realization of multiplier Hilbert bimodule on bidual space and Tietze extension theorem, Chinese Ann. Math Ser. B 21(2000), 375-380. MR 1788294 (2001h:46108)
  • 5. C. Lance, Hilbert $C^*$-modules: a toolkit for operator algebraists, London Math. Soc. Lecture Notes Series, vol. 210, Cambridge University Press, Cambridge, 1995. MR 1325694 (96k:46100)
  • 6. I. Raeburn, D. P. Williams, Morita equivalence and continuous-trace $C^*$-algebras, Mathematical Surveys and Monographs 60, AMS, 1998. MR 1634408 (2000c:46108)
  • 7. N. E. Wegge-Olsen, K-theory and $C^*$-algebras, Oxford University Press, Oxford, 1993. MR 1222415 (95c:46116)

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Additional Information

Damir Bakic
Affiliation: Department of Mathematics, University of Zagreb, Bijenička cesta 30, P.O.Box 335, 10002 Zagreb, Croatia
Email: bakic@math.hr

DOI: https://doi.org/10.1090/S0002-9939-04-07563-X
Keywords: $C^*$-algebra, Tietze extension theorem, Hilbert $C^*$-module
Received by editor(s): December 3, 2002
Received by editor(s) in revised form: July 11, 2003
Published electronically: August 25, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society

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