Discrete spectra of $C^{*}$-algebras and orthogonally closed submodules in Hilbert $C^{*}$-modules
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- by Masaharu Kusuda PDF
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Abstract:
Let $A$ and $B$ be $C^{*}$-algebras and let $X$ be an $A$-$B$-imprimitivity bimodule. Then it is shown that if the spectrum $\widehat A$ of $A$ (resp. $\widehat B$ of $B$) is discrete, then every closed $A$-$B$-submodule of $X$ is orthogonally closed in $X$, and conversely that if $\widehat A$ (resp. $\widehat B$) is a $T_{1}$-space and if every closed $A$-$B$-submodule of $X$ is orthogonally closed in $X$, then $\widehat A$ (resp. $\widehat B$) is discrete.References
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Additional Information
- Masaharu Kusuda
- Affiliation: Department of Mathematics, Faculty of Engineering, Kansai University, Yamate-cho 3-3-35, Suita, Osaka 564-8680, Japan
- Email: kusuda@ipcku.kansai-u.ac.jp
- Received by editor(s): December 3, 2003
- Received by editor(s) in revised form: June 23, 2004
- Published electronically: May 9, 2005
- Communicated by: David R. Larson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3341-3344
- MSC (2000): Primary 46L05, 46L08
- DOI: https://doi.org/10.1090/S0002-9939-05-07909-8
- MathSciNet review: 2161158