Zynab IZADI, Rahmat SOLTANI

Maps on S(H) preserving the difference of noninvertible algebraic operators

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

The aim of this paper is to present the general structure of nonlinear surjective maps on S(H) preserving the operator pairs in which their difference is a noninvertible algebraic operator. S(H) represents the real Jordan algebra of bounded self-adjoint operators acting on an infinite dimensional Hilbert space H.

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[1] Bourhim A, Mashreghi J, Stepanyan A. Non-linear maps preserving the minimum and surjectivity moduli. Linear Algebra and its Applications 2014; 463: 171-189.
[2] Costara C, Repovs D. Non-linear mappings preserving at least one eigenvalue. Studia Mathematica 2010; 200: 79-89.
[3] Havlicek H, Semrl P. From geometry to invertibility preserves. Studia Mathematica 2006; 174: 99-109.
[4] Oudghiri M, Souilah K. Non-linear maps preserving singular algebraic operators. Proyecciones Journal of Mathematics 2016; 35: 301-316.
[5] Pearcy C, Topping D. Sums of small numbers of idempotents. Michigan Mathematical Journal 1967; 14: 453-465.
[6] Petek T, Semrl P. Adjacency preserving maps on matrices and operators. Proceedings of the Royal Society of Edinburgh, Section A Mathematics 2002; 132: 661-684.
[7] Semrl P. Symmetries on bounded observables: a unified approach based on adjacency preserving maps. Integral Equations and Operator Theory 2012; 72: 7-66.