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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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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: http://dx.doi.org/10.1090/S0002-9939-04-07563-X
PII: S 0002-9939(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