Abstract. We prove that any bijective map between the positive definite cones of von Neumann algebras which preserves a certain unitarily invariant norm of a particular weighted geometric mean of elements is essentially (up to two-sided multiplication by an invertible positive element) equal to the restriction of a Jordan *-isomorphism between the algebras.

DOI: 10.14232/actasm-018-514-x

AMS Subject Classification (1991): 47B49; 46L40, 47A64

Keyword(s): positive definite cone, operator means, geodesic correspondence, preservers

Received January 18, 2018 and in final form February 23, 2018. (Registered under 14/2018.)