Maps preserving the geometric mean of positive operators.

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]