A generalized notion of orthogonality preserving mappings on inner product modules

Document Type : Research Paper

Author

Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran

Abstract

‎‎‎‎‎In this paper, we define a new concept called ``strongly orthogonality preserving mappings '' for inner product modules, which extends the existing notion of ``orthogonality preserving mappings". Also, we provide a condition that is both necessary and sufficient for a linear map between inner product modules to be strongly orthogonality preserving. Some examples on the definition are given.

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References

[1] Frank, M., Mishchenko, A. S., & Pavlov, A. A. (2011). Orthogonality preserving, $C^*-$conformal and conformal module mappings on Hilbert $C^*-$modules. J. Funct. Anal., 260, 327-339. https://doi.org/10.1016/j.jfa.2010.10.009.
[2] Ilisevic, D., & Turnsek, A. (2008). Approximately orthogonality preserving mappings on $C^*-$modules. J. Math. Anal. Appl., 341, 298-308. https://doi.org/10.1016/j.jmaa.2007.10.028.
[3] Khoddami, A. R. (2015). On maps preserving strongly zero-products. Chamchuri J. Math., 7, 16-23.  http://www.math.sc.chula.ac.th/cjm.
[4] Leung, C.-W., Ng, C.-K., & Wong, N.-C. (2012). Linear orthogonality preservers of Hilbert $C^*-$modules over $C^*-$algebras with real rank zero. Proc. Amer. Math. Soc., 140(9), 3151-3160. https://www.jstor.org/stable/41635428.
[5] Moslehian, M. S., Zamani, A., & Frank, M. (2015). Angle preserving mappings. Z. Anal. Anwend, 34(4), 485-500.  https://doi.org/10.4171/ZAA/1551.
[6] Murphy, G. J. (1990). $C^*-$Algebras and Operator Theory, Academic Press, New York.

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History

  • Receive Date: 15 September 2023
  • Revise Date: 02 December 2023
  • Accept Date: 09 December 2023

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