33 citations · 55 across the 19 of their papers we have counts for
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Horofunction compactifications of symmetric cones under Finsler distances
Bas Lemmens
In this paper we consider symmetric cones as symmetric spaces equipped with invariant Finsler distances, namely the Thompson distance and the Hilbert distance. We establish a corre…
Hilbert and Thompson isometries on cones in JB-algebras
Bas Lemmens, Mark Roelands, Marten Wortel
Hilbert's and Thompson's metric spaces on the interior of cones in JB-algebras are important examples of symmetric Finsler spaces. In this paper we characterize the Hilbert's metri…
Midpoints for Thompson's metric on symmetric cones
Bas Lemmens, Mark Roelands
We characterise the affine span of the midpoints sets for Thompson's metric on symmetric cones in terms of a translation of the zero-component of the Peirce decomposition of an ide…
Isometries of infinite dimensional Hilbert geometries
Bas Lemmens, Mark Roelands, Marten Wortel
In this paper we extend results by De la Harpe concerning the isometries of strictly convex Hilbert geometries, and the characterisation of the isometry groups of Hilbert geometrie…
Unique geodesics for Thompson's metric
Bas Lemmens, Mark Roelands
In this paper a geometric characterization of the unique geodesics in Thompson's metric spaces is presented. This characterization is used to prove a variety of other geometric res…
Birkhoff's version of Hilbert's metric and its applications in analysis
Bas Lemmens, Roger Nussbaum
This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the "Han…