International Journal of Nonlinear Analysis and Applications

On fuzzy C*-algebras

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 show that there is no fuzzy $C^*$-lgebra norm according to the definitions contained in [1, 2, 3]‎. ‎Based on our claim‎, ‎some parts of [Theorems 2 and 3, 2],  [Corollaries 1 and 2, 2] and [Theorem 4, 3] are incorrect‎.

Keywords

[1] N. Ansari, M.H. Hooshmand, M.E. Gordji, and K. Jahedi, Stability of fuzzy orthogonally ∗−n−derivation in orthogonally fuzzy C*−algebras, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 1, 533–540.
[2] P. Lolo, E. Movahednia, and M. De la Sen, Hyers stability and multi-fuzzy Banach algebra, Mathematics 10 (2022), 1–13.
[3] E. Movahednia and M. De la Sen, A new approach to involution in fuzzy C*−algebra via functional inequality and Python implementation, Axioms 12 (2023), 1–14.
[4] C. Park, J.R. Lee, T.M. Rassias, and R. Saadati, Fuzzy ∗−homomorphisms and fuzzy ∗−derivations in induced fuzzy C*−algebras, Math. Comput. Model. 54 (2011), 2027–2039.
International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 4
April 2025
Pages 229-231
  • Receive Date: 21 September 2023
  • Revise Date: 02 February 2024
  • Accept Date: 24 February 2024