Isometries of Hilbert $C^*$-modules
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- by Baruch Solel
- Trans. Amer. Math. Soc. 353 (2001), 4637-4660
- DOI: https://doi.org/10.1090/S0002-9947-01-02874-4
- Published electronically: July 3, 2001
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Abstract:
Let $X$ and $Y$ be right, full, Hilbert $C^*$-modules over the algebras $A$ and $B$ respectively and let $T:X\to Y$ be a linear surjective isometry. Then $T$ can be extended to an isometry of the linking algebras. $T$ then is a sum of two maps: a (bi-)module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-)module actions. If $A$ (or $B$) is a factor von Neumann algebra, then every isometry $T:X\to Y$ is either a (bi-)module map or reverses the (bi-)module actions.References
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Bibliographic Information
- Baruch Solel
- Affiliation: Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
- Email: mabaruch@techunix.technion.ac.il
- Received by editor(s): June 26, 2000
- Published electronically: July 3, 2001
- Additional Notes: Supported by Technion V.P.R. Fund–Steigman Research Fund, Technion V.P.R. Fund–Fund for the Promotion of Sponsored Research and the Fund for the Promotion of Research at the Technion.
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 4637-4660
- MSC (2000): Primary 46L08
- DOI: https://doi.org/10.1090/S0002-9947-01-02874-4
- MathSciNet review: 1851186