A REPRESENTATION THEOREM FOR LYAPUNOV-LIKE TRANSFORMATIONS ON EUCLIDEAN JORDAN ALGEBRAS

Jiyuan Tao () and M. Seetharama Gowda ()
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Jiyuan Tao: Department of Mathematics and Statistics, Loyola University Maryland, Baltimore, Maryland 21210, USA
M. Seetharama Gowda: Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA

International Game Theory Review (IGTR), 2013, vol. 15, issue 04, 1-11

Abstract: A Lyapunov-like (linear) transformationLon a Euclidean Jordan algebraVis defined by the condition$$x \in K,\enspace y\in K^*,\quad \langle x,y\rangle =0\Rightarrow \langle L(x),y\rangle=0,$$whereKis the symmetric cone ofV. In this paper, we give an elementary proof (avoiding Lie algebraic ideas and results) of the fact that Lyapunov-like transformations onVare of the formLa+ D, wherea ∈ V,Dis a derivation, andLa(x) = a ◦ xfor allx ∈ V.

Keywords: Euclidean Jordan algebra; symmetric cone; Zand Lyapunov-like transformations; 90C33; 17C55; 15A48 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219198913400343

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