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Journal of Lie Theory 30 (2020), No. 2, 461--471
Copyright Heldermann Verlag 2020

A Banach Algebra Approach to Loos Symmetric Cones

Jimmie Lawson
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.

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.

Keywords: Loos symmetric cone, normal cone, symmetric space, Banach-Lie group, involutive group.

MSC: 53C35; 47L10, 22E65.

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