Automorphism Invariance of P- and GUS-Properties of Linear Transformations on Euclidean Jordan Algebras

Authors:
M. Seetharama Gowda;Roman Sznajder
Affiliations:
Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, Maryland 21250;Department of Mathematics, Bowie State University, Bowie, Maryland 20715-9465
Venue:
Mathematics of Operations Research
Year:
2006

Citing 1
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Abstract

Generalizing the P-property of a matrix, Gowda et al. [Gowda, M. S., R. Sznajder, J. Tao. 2004. Some P-properties for linear transformations on Euclidean Jordan algebras. Linear Algebra Appl.393 203232] recently introduced and studied P- and globally uniquely solvable (GUS)-properties for linear transformations defined on Euclidean Jordan algebras. In this paper, we study the invariance of these properties under automorphisms of the algebra and of the symmetric cone. By means of these automorphisms and the concept of a principal subtransformation, we introduce and study ultra and super P-(GUS)-properties for a linear transformation on a Euclidean Jordan algebra.