On the finiteness of the cone spectrum of certain linear transformations on Euclidean Jordan algebras
نویسندگان
چکیده
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)− λx ∈ 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 .
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