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

✍ Scribed by Yihui Zhou; M. Seetharama Gowda

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
179 KB
Volume
431
Category
Article
ISSN
0024-3795

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✦ Synopsis

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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