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December 2007 Metric convexity of symmetric cones
Jimmie Lawson, Yongdo Lim
Osaka J. Math. 44(4): 795-816 (December 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 geodesics is a convex function. This provides an affirmative answer to a question of Neeb [22].

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Jimmie Lawson. Yongdo Lim. "Metric convexity of symmetric cones." Osaka J. Math. 44 (4) 795 - 816, December 2007.

Information

Published: December 2007
First available in Project Euclid: 7 January 2008

zbMATH: 1135.53014
MathSciNet: MR2383810

Subjects:
Primary: 46B20 , 47H07 , 53B40 , 53C35

Rights: Copyright © 2007 Osaka University and Osaka City University, Departments of Mathematics

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Vol.44 • No. 4 • December 2007
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