On some Finsler structures of symmetric cones (Q2753157)

The authors study the Finsler metric defined on the domain of positive invertible elements of a \(C^*\)-algebra, which is faithfully represented in a Hilbert space. This domain is a special case of a symmetric cone from JB-algebras, the selfadjoint part of JB*-algebras. They consider only the finite-dimensional case.NEWLINENEWLINENEWLINEThe main results: 1) Determination of some Finsler metrics on the symmetric cones in the context of \textit{G. Corach}, \textit{H. Porta} and \textit{L. Recht} [Proc. Am. Math. Soc. 115, 229-231 (1992; Zbl 0749.58010); Int. J. Math. 4, 193-202 (1993; Zbl 0809.47017)]. 2) A symmetric cone \(\Omega\) has some sort of nonpositive curvature with respect to the considered Finsler metric.