Geodesic
A Banach Algebra Approach to Loos Symmetric Cones
Journal of Lie theory, Tome 30 (2020) no. 2, pp. 461-471
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We consider Loos symmetric spaces on an open cone Ω in the Banach space setting and show how such Loos symmetric spaces may be realized from the set of elements inverted by an involution on a Banach-Lie group. The group is a subgroup of the group of invertible elements of the Banach algebra of all bounded linear transformations on the Banach space V = Ω - Ω. This construction connects the theory of Loos symmetric cones to that of involutive Lie groups.
Classification : 53C35, 47L10, 22E65
Mots-clés : Loos symmetric cone, normal cone, symmetric space, Banach-Lie group, involutive group 
@article{JLT_2020_30_2_JLT_2020_30_2_a9,
     author = {J. Lawson},
     title = {A {Banach} {Algebra} {Approach} to {Loos} {Symmetric} {Cones}},
     journal = {Journal of Lie theory},
     pages = {461--471},
     year = {2020},
     volume = {30},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a9/}
}
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J. Lawson. A Banach Algebra Approach to Loos Symmetric Cones. Journal of Lie theory, Tome 30 (2020) no. 2, pp. 461-471. http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a9/