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arXiv 1609.034732016-09math.MGmath.FAmath.OA

JB-代数锥上的Hilbert和Thompson等距映射

Hilbert and Thompson isometries on cones in JB-algebras

Bas Lemmens, Mark Roelands, Marten Wortel

备注：: 36 pages
发表信息：: Math. Z. 292 (2019), no. 3-4, 1511 - 1547

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AI总结：

本文刻画了JBW-代数和JB-代数锥内部的Hilbert与Thompson度量等距映射，推广了已有在对称锥及$C^*$-代数上的相关工作，并发展了新的几何与Jordan代数技巧。

摘要：

JB-代数锥内部的Hilbert和Thompson度量空间是对称Finsler空间的重要实例。本文刻画了JBW-代数锥内部的Hilbert度量等距映射，以及JB-代数锥内部的Thompson度量等距映射。这些刻画推广了Bosché关于对称锥上Hilbert和Thompson等距映射的工作，以及Hatori和Molnár关于有单位元的$C^*$-代数中正自伴元素锥上Thompson等距映射的工作。为获得这些结果，我们发展了多种新的几何与Jordan代数技巧。

英文摘要：

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 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 and Thompson isometries on symmetric cones, and work by Hatori and Molnár on the Thompson isometries on the cone of positive self-adjoint elements in a unital $C^*$-algebra. To obtain the results we develop a variety of new geometric and Jordan algebraic techniques.

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