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Orthogonality preserving property, Wigner equation, and stability
Journal of Inequalities and Applications volume 2006, Article number: 76489 (2006)
Abstract
We deal with the stability of the orthogonality preserving property in the class of mappings phase-equivalent to linear or conjugate-linear ones. We give a characterization of approximately orthogonality preserving mappings in this class and we show some connections between the considered stability and the stability of the Wigner equation.
References
Almeida DF, Sharma CS: The first mathematical proof of Wigner's theorem. Journal of Natural Geometry 1992,2(2):113–123.
Chmieliński J: On a singular case in the Hyers-Ulam-Rassias stability of the Wigner equation. Journal of Mathematical Analysis and Applications 2004,289(2):571–583. 10.1016/j.jmaa.2003.08.042
Chmieliński J: Linear mappings approximately preserving orthogonality. Journal of Mathematical Analysis and Applications 2005,304(1):158–169. 10.1016/j.jmaa.2004.09.011
Chmieliński J: Stability of angle-preserving mappings on the plane. Mathematical Inequalities & Applications 2005,8(3):497–503.
Chmieliński J: Stability of the orthogonality preserving property in finite-dimensional inner product spaces. Journal of Mathematical Analysis and Applications 2006,318(2):433–443. 10.1016/j.jmaa.2005.06.016
Chmieliński J: Stability of the Wigner equation and related topics. to appear in Nonlinear Functional Analysis and Applications, special issue dedicated to the memory of D. H. Hyers to appear in Nonlinear Functional Analysis and Applications, special issue dedicated to the memory of D. H. Hyers
Hyers DH, Isac G, Rassias TM: Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and Their Applications. Volume 34. Birkhäuser Boston, Massachusetts; 1998:vi+313.
Jung S-M: Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, Florida; 2001:ix+256.
Jung S-M: Hyers-Ulam stability of Butler-Rassias functional equation. Journal of Inequalities and Applications 2005,2005(1):41–47. 10.1155/JIA.2005.41
Miura T, Takahasi S-E, Hirasawa G: Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras. Journal of Inequalities and Applications 2005,2005(4):435–441. 10.1155/JIA.2005.435
Rätz J: On Wigner's theorem: remarks, complements, comments, and corollaries. Aequationes Mathematicae 1996,52(1–2):1–9.
Uhlhorn U: Representation of symmetry transformations in quantum mechanics. Arkiv Fysik 1963, 23: 307–340.
Wigner EP: Gruppentheorie und ihre Anwendungen auf die Quantenmechanik der Atomspektren. Friedrich Vieweg und Sohn Akt.-Ges., Braunschweig; 1931.
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Chmieliński, J. Orthogonality preserving property, Wigner equation, and stability. J Inequal Appl 2006, 76489 (2006). https://doi.org/10.1155/JIA/2006/76489
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DOI: https://doi.org/10.1155/JIA/2006/76489
Keywords
- Preserve Mapping
- Preserve Property
- Wigner Equation
- Orthogonality Preserve
- Orthogonality Preserve Property