Abstract
Let V be a Euclidean Jordan algebra with identity e, and let Ω be the corresponding symmetric cone. In this paper, we introduce a partially ordered commutative semigroup structure on the closed convex cone extending the binary operation a : b = (a–1 + b–1)–1 on Ω and consider compressions of the symmetric cone Ω of the form where P is the quadratic representation of the Jordan algebra V and Aut(V) is the Jordan automorphism group of V. The aim of this paper is to show that Φa,b,kP(w) has a unique fixed point p(a, b, kP(w)) on Ω and the fixed point map is continuous.
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