Connects Loos symmetric spaces and involutive Lie groups in Banach spaces, implying a new perspective on cone theory.
We consider Loos symmetric spaces on an open cone 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 = - .This construction connects the theory of Loos symmetric cones to that of involutive Lie groups.
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J. D. Lawson (2020) studied this question.
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