Abstract:Let $H$ be a complex Hilbert space. The symbol $A\# B$ stands for the geometric mean of the positive bounded linear operators $A,B$ on $H$ in the sense of Ando. In this paper we describe the general form of all automorphisms of the set of positive operators with respect to the operation $\#$. We prove that if $\dim H\geq 2$, any such transformation is implemented by an invertible bounded linear or conjugate-linear operator on $H$.
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- Lajos Molnár
- Affiliation: Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary
- Email: firstname.lastname@example.org
- Received by editor(s): November 13, 2007
- Received by editor(s) in revised form: June 27, 2008
- Published electronically: December 11, 2008
- Additional Notes: The author was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T046203, NK68040 and by the Alexander von Humboldt Foundation, Germany.
- Communicated by: Marius Junge
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 137 (2009), 1763-1770
- MSC (2000): Primary 47B49, 47A64
- DOI: https://doi.org/10.1090/S0002-9939-08-09749-9
- MathSciNet review: 2470835