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Similarity automorphism invariance of some P-properties of linear transformations on Euclidean Jordan algebras

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Abstract

Recently, Gowda and Sznajder [Gowda, M.S., Sznajder, R.: Automorphism invariance of P- and GUS-properties of linear transformations on Euclidean Jordan algebras. Math. Oper. Res. 31, 109–123 (2006)] have introduced and studied automorphism invariance of some P-properties for linear transformations. This paper deals with this automorphism invariance of some other complementarity properties, such as \(\hbox {E}_0,\,\hbox {P}_0\), S, Z-properties. Particularly, we answer Gowda and Sznajder in positive that order P-property is algebra automorphism invariant in simple Jordan algebras. By replacing transposition with the invertibility in the concept of automorphism invariance, we propose a notion of similarity automorphism invariance. Most complementarity properties of linear transformations are also shown to be similarity invariant under algebra automorphisms and cone automorphisms.

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Acknowledgments

The authors are very grateful to the editor and the anonymous referee for their valuable suggestions. This work is supported partially by National Natural Science Foundation of China (Grant No. 61301283) and by Fundamental Research Funds for the Central Universities (Grant Nos. K5051370006, K5051370024, and K5051370011).

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  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, People’s Republic of China

    Yuan Min Li & Deyun Wei

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  1. Yuan Min Li
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  2. Deyun Wei
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Correspondence to Yuan Min Li.

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Li, Y.M., Wei, D. Similarity automorphism invariance of some P-properties of linear transformations on Euclidean Jordan algebras. Optim Lett 8, 2087–2098 (2014). https://doi.org/10.1007/s11590-013-0710-x

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