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Isometries of the unitary group


Authors: Osamu Hatori and Lajos Molnár
Journal: Proc. Amer. Math. Soc. 140 (2012), 2127-2140
MSC (2010): Primary 47B49
DOI: https://doi.org/10.1090/S0002-9939-2011-11216-4
Published electronically: October 21, 2011
MathSciNet review: 2888199
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Abstract: In this paper we describe all surjective isometries of the unitary group of a complex Hilbert space. A result on Thompson isometries of the space of all invertible positive elements of a unital $ C^*$-algebra is also presented.


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Additional Information

Osamu Hatori
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan
Email: hatori@math.sc.niigata-u.ac.jp

Lajos Molnár
Affiliation: Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary
Email: molnarl@science.unideb.hu

DOI: https://doi.org/10.1090/S0002-9939-2011-11216-4
Keywords: Unitary group, Hilbert space, isometry, Mazur-Ulam theorem, $C^{*}$-algebra, Thompson metric
Received by editor(s): February 12, 2011
Published electronically: October 21, 2011
Additional Notes: The first author was partly supported by the Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science.
The second author was supported by the Alexander von Humboldt Foundation (Germany), by the Hungarian Scientific Research Fund (OTKA) K81166 NK81402, and by the TÁMOP 4.2.1./B-09/1/KONV-2010-0007 project implemented through the New Hungary Development Plan co-financed by the European Social Fund and the European Regional Development Fund.
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.