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http://dx.doi.org/10.14317/jami.2016.309

CHARACTERIZATION OF GLOBALLY-UNIQUELY-SOLVABLE PROPERTY OF A CONE-PRESERVING Z-TRANSFORMATION ON EUCLIDEAN JORDAN ALGEBRAS  

SONG, YOON J. (Department of Mathematics, Soongsil University)
Publication Information
Journal of applied mathematics & informatics / v.34, no.3_4, 2016 , pp. 309-317 More about this Journal
Abstract
Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation SA(X) := X - AXAT on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that SA GUS ⇔ I ± A positive definite.
Keywords
Euclidean Jordan algebra; Stein transformation; P-property; Strictly copositive; GUS-property; Monotone;
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Times Cited By KSCI : 2  (Citation Analysis)
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