On the finiteness of the cone spectrum of certain linear transformations on Euclidean Jordan algebras

AbstractLet L be a linear transformation on a finite dimensional real Hilbert space H and K be a closed convex cone with dual K∗ in H. The cone spectrum of L relative to K is the set of all real λ for which the linear complementarity problemx∈K,y=L(x)-λx∈K∗,and〈x,y〉=0admits a nonzero solution x. In the setting of a Euclidean Jordan algebra H and the corresponding symmetric cone K, we discuss the finiteness of the cone spectrum for Z-transformations and quadratic representations on H

On the finiteness of the cone spectrum of certain linear transformations on Euclidean Jordan algebras

Let L be a linear transformation on a finite dimensional real Hilbert space H and K be a closed convex cone with dual K ∗ in H . The cone spectrum of L relative to K is the set of all real λ for which the linear complementarity problem x ∈ K , y = L ( x ) - λ x ∈ K ∗ , and 〈 x , y 〉 = 0 admits a nonzero solution x . In the setting of a Euclidean Jordan algebra H and the corresponding symmetric cone K , we discuss the finiteness of the cone spectrum for Z -transformations and quadratic representations on H

Local minima of quadratic forms on convex cones

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