Stability of the Neutrosophic Spectrum and Fredholm Operators under Compact Perturbations

Karima Y.  Elzalouk

المؤلفون

Karima Y. Elzalouk كلية العلوم جامعة مصراتة

الكلمات المفتاحية:

Neutrosophic Banach space، compact perturbation، Fredholm operator، neutrosophic spectrum، spectral stability

الملخص

We study the stability of bounded linear operators in generalized neutrosophic Banach spaces under small and compact perturbations. A triple-valued framework based on truth, indeterminacy, and falsity is introduced to govern convergence and operator perturbation in the neutrosophic setting. We define neutrosophic perturbation operators, establish stability criteria for invertibility, and develop a Fredholm-type theory for neutrosophic bounded operators. In particular, we prove that the neutrosophic spectrum is stable under sufficiently small compact perturbations and that the neutrosophic Fredholm index remains invariant. These results move beyond the already established boundedness-continuity theme and provide a structural basis for neutrosophic spectral analysis.

المراجع

Akashi, W. Y. (1984). On the perturbation theory for Fredholm operators. Osaka Journal of Mathematics, 21(3), 603–612.

Bera, T., & Mahapatra, N. K. (2020). On neutrosophic soft normed linear space. Journal of Intelligent & Fuzzy Systems, 39(1), 615–628.

Chaurasiya, C., Ahmad, A., Shankar, H., & Singh, R. (2025). Exploring bounded linear operators in neutrosophic normed linear spaces. Fuzzy Information and Engineering, 17(1), 39–58. doi:10.26599/FIE.2025.9270052.

Douglas, R. G. (1998). Compact operators, Fredholm operators, and index theory (2nd ed.). Springer-Verlag.

Fari, M. J. (2026). A study on structural properties of operators in neutrosophic Banach spaces. Journal of the College of Basic Education, 32(135), 58–67. doi:10.35950/cbej.v32i135.14610.

Fari, M. J., Bagheedh, A. K., & Hussein, F. S. (2026). Exploring some fundamental properties of operators in neutrosophic Banach spaces. Boletim da Sociedade Paranaense de Matemática, 44, 1–10. doi:10.4025/bsmp.v44.81520.

Higgins, D. J. (1972). Notes on Fredholm and compact operators. The American Mathematical Monthly, 79(3), 250–264.

Kato, T. (1980). Perturbation theory for linear operators. Springer-Verlag.

Omran, S., & Elrawy, A. (2021). Continuous and bounded operators on neutrosophic normed spaces. Neutrosophic Sets and Systems, 46(1), 1–13.

Pandiselvi, M., & Jeyaraman, M. (2024). Exploring topological characteristics of neutrosophic Banach spaces. Neutrosophic Sets and Systems, 69, 146–155.

Schweizer, B., & Sklar, A. (1983). Probabilistic metric spaces. Elsevier Science Publishing.

Smarandache, F. (1998). A unifying field in logics. neutrosophy: Neutrosophic probability, set and logic. American Research Press.