Abstract:
Hilbert’s and Thompson’s metric spaces on the interior of cones in JB-algebras are important
examples of symmetric Banach-Finsler spaces. In this paper we characterize the Hilbert’s
metric isometries on the interiors of cones in JBW-algebras, and the Thompson’s metric
isometries on the interiors of cones in JB-algebras. These characterizations generalize work
by Bosché on the Hilbert’s and Thompson’s metric isometries on symmetric cones, and work
by Hatori and Molnár on the Thompson’s metric isometries on the cone of positive selfadjoint
elements in a unital C∗-algebra. To obtain the results we develop a variety of new
geometric and Jordan algebraic techniques.
