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Maps preserving the geometric mean of positive operators.
- Source :
-
Proceedings of the American Mathematical Society . Dec2008, Vol. 137 Issue 5, p1763-1770. 8p. - Publication Year :
- 2008
-
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 $dim Hgeq 2$, any such transformation is implemented by an invertible bounded linear or conjugate-linear operator on $H$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 137
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 36177265
- Full Text :
- https://doi.org/10.1090/S0002-9939-08-09749-9