Tietze extension theorem for Hilbert $C^*$-modules
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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
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Additional Information
- Damir Bakić
- Affiliation: Department of Mathematics, University of Zagreb, Bijenička cesta 30, P.O.Box 335, 10002 Zagreb, Croatia
- Email: bakic@math.hr
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2093066