Geodesic
A Banach Algebra Approach to Loos Symmetric Cones
Jimmie Lawson1
1Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Journal of Lie Theory, Tome 30 (2020) no. 2, pp. 461-471

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Jimmie Lawson  1

1 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A. 
Jimmie 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/JOLT_2020_30_2_a9/
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     author = {Jimmie 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/JOLT_2020_30_2_a9/}
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