
Journal of Lie Theory 30 (2020), No. 2, 461471 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. lawson@math.lsu.edu 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 BanachLie 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, BanachLie group, involutive group. MSC: 53C35; 47L10, 22E65. [ Fulltextpdf (120 KB)] for subscribers only. 