Title

Metric convexity of symmetric cones

Document Type

Article

Publication Date

12-1-2007

Abstract

In this paper we introduce a general notion of a symmetric cone, valid for the finite and infinite dimensional case, and prove that one can deduce the seminegative curvature of the Thompson part metric in this general setting, along with standard inequalities familiar from operator theory. As a special case, we prove that every symmetric cone from a JB-algebra satisfies a certain convexity property for the Thompson part metric: the distance function between points evolving in time on two geodesies is a convex function. This provides an affirmative answer to a question of Neeb [22].

Publication Source (Journal or Book title)

Osaka Journal of Mathematics

First Page

795

Last Page

816

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