Isometries of Hilbert 
-modules
Author:
Baruch Solel
Journal:
Trans. Amer. Math. Soc. 353 (2001), 4637-4660
MSC (2000):
Primary 46L08
DOI:
https://doi.org/10.1090/S0002-9947-01-02874-4
Published electronically:
July 3, 2001
MathSciNet review:
1851186
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Let 
and 
be right, full, Hilbert 
-modules over the algebras 
and 
respectively and let 
be a linear surjective isometry. Then 
can be extended to an isometry of the linking algebras. 
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 
(or 
) is a factor von Neumann algebra, then every isometry 
is either a (bi-)module map or reverses the (bi-)module actions.
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Additional Information
Baruch Solel
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
Email:
mabaruch@techunix.technion.ac.il
DOI:
https://doi.org/10.1090/S0002-9947-01-02874-4
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.
Article copyright:
© Copyright 2001
American Mathematical Society