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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
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.

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  • 1. Damir Bakić and Boris Guljaš, On a class of module maps of Hilbert 𝐶*-modules, Math. Commun. 7 (2002), no. 2, 177–192. MR 1952758
  • 2. D. Bakic, B. Guljas, Extensions of Hilbert $C^*$-modules, to appear in Houston J. Math.
  • 3. Lawrence G. Brown, Philip Green, and Marc A. Rieffel, Stable isomorphism and strong Morita equivalence of 𝐶*-algebras, Pacific J. Math. 71 (1977), no. 2, 349–363. MR 0463928
  • 4. Xiaochun Fang, The realization of multiplier Hilbert bimodule on bidual space and Tietze extension theorem, Chinese Ann. Math. Ser. B 21 (2000), no. 3, 375–380. MR 1788294, 10.1142/S025295990000039X
  • 5. E. C. Lance, Hilbert 𝐶*-modules, London Mathematical Society Lecture Note Series, vol. 210, Cambridge University Press, Cambridge, 1995. A toolkit for operator algebraists. MR 1325694
  • 6. Iain Raeburn and Dana P. Williams, Morita equivalence and continuous-trace 𝐶*-algebras, Mathematical Surveys and Monographs, vol. 60, American Mathematical Society, Providence, RI, 1998. MR 1634408
  • 7. N. E. Wegge-Olsen, 𝐾-theory and 𝐶*-algebras, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993. A friendly approach. MR 1222415

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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

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