An innovation analytical application of the proposed system of equations on Hilbert space
*Salim Dawood MohsenCorresponding authordr_salim2015@yahoo.comDepartment of Mathematics College of Education Mustensiriyah UniversityDepartment of Mathematics College of Education Mustansiriyah UniversityBaghdad, 10052, Iraqhttps://orcid.org/0000-0002-4435-4658View full profile → , Ihsan Abdulsattar Awadhahsan.123.amani1989@gmail.comDepartment of Mathematics College of Education Mustensiriyah UniversityBaghdad, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Dec 2024
- Published Online:
- 08 May 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2207
- Pages:
- 1185–1196
Abstract
Keywords
Subject Classifications
References
[1] Y. Tian, “The solvability of two linear matrix equations,” Linear Multilinear Algebra, vol. 48, no. 2, pp. 123–147 (2000).
[2] D. C. Sorensen and A. C. Antoulas, “The Sylvester equation and approximate balanced reduction,” Linear Algebra Appl., vol. 351, pp. 671–700 (2002).
[3] F. Piao, Q. Zhang, and Z. Wang, “The solution to matrix equation AX+XTC=BAX+XTC=B,” J. Franklin Inst., vol. 344, no. 8, pp. 1056–1062 (2007).
[4] Q. W. Wang and C. K. Li, “Ranks and the least-norm of the general solution to a system of quaternion matrix equations,” Linear Algebra Appl., vol. 430, no. 5–6, pp. 1626–1640 (2009).
[5] M. Dehghan and M. Hajarian, “The general coupled matrix equations over generalized bisymmetric matrices,” Linear Algebra Appl., vol. 432, no. 6, pp. 1531–1552 (2010).
[6] Q. W. Wang, X. Zhang, and J. W. van der Woude, “A new simultaneous decomposition of a matrix quaternity over an arbitrary division ring with applications,” Commun. Algebra, vol. 40, no. 7, pp. 2309–2342 (2012).
[7] S. D. Mohsen, “New generalizations for MM-hyponormal operators,” Iraqi J. Sci., pp. 6477–6482 (2023).
[8] S. D. Mohsen, “Solvability of (λ,μ)(λ,μ)-commuting operator equations for bounded generalization of hyponormal operators,” Iraqi J. Sci., vol. 63, no. 9, pp. 3854–3860 (2022).
[9] C. G. Khatri and S. K. Mitra, “Hermitian and nonnegative definite solutions of linear matrix equations,” SIAM J. Appl. Math., vol. 31, no. 4, pp. 579–585 (1976).
[10] A. Dajić and J. J. Koliha, “Positive solutions to the equations AX=CAX=C and XB=DXB=D for Hilbert space operators,” J. Math. Anal. Appl., vol. 333, no. 2, pp. 567–576 (2007).
[11] Q. Wang, H. Chang, and C. Lin, “On the centro-symmetric solution of a system of matrix equations over a regular ring with identity,” Algebra Colloq., pp. 555–570 (2007).
[12] F. O. Farid, M. S. Moslehian, Q. W. Wang, and Z. C. Wu, “On the Hermitian solutions to a system of adjointable operator equations,” Linear Algebra Appl., vol. 437, no. 7, pp. 1854–1891 (2012).
[13] C. Deng, “On the solutions of operator equation CAX=C=XACCAX =C=XAC,” J. Math. Anal. Appl., vol. 398, no. 2, pp. 664–670 (2013).
[14] M. Vosough and M. S. Moslehian, “Solutions of the system of operator equations BXA=B=AXBBXA=B=AXB via ∗∗-order,” arXiv Prepr., arXiv:1705.07037 (2017).
[15] P. Bhimasankaram, “Common solutions to the linear matrix equations AX=CAX=C, XB=DXB=D, and FXG=HFXG=H,” Sankhyā, Indian J. Stat., Ser. A, pp. 404–409 (1976).
[16] X. Zhang and J. Guoxing, “Solutions to the system of operator equations AXB=C=BXAAXB=C=BXA,” Acta Math. Sci., vol. 38, no. 4, pp. 1143–1150 (2018).
[17] S. D. Mohsen and N. M. Atheab, “Some results on (ℵ,k)(ℵ,k)-hyponormal operators,” J. Phys. Conf. Ser., vol. 1591, no. 1, p. 012064 (2020).
[18] Q. W. Wang, “The general solution to a system of real quaternion matrix equations,” Comput. Math. Appl., vol. 49, no. 5–6, pp. 665–675 (2005).
[19] S. D. Mohsen and Y. H. Thiyab, “Some characteristics of completeness property in fuzzy soft bb-metric space,” J. Appl. Sci. Eng., vol. 27, no. 3, pp. 2227–2232 (2023).
[20] Y. X. Peng, X. Y. Hu, and L. Zhang, “An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB=CAXB=C,” Appl. Math. Comput., vol. 160, no. 3, pp. 763–777ℵ2005).
[21] S. D. Mohsen, “Novel results of KK-quasi (Γ−M)-hyponormal operator,” Iraqi J. Sci., pp. 374–380ℵ2024).
[22] S. D. Mohsen, “On−n(k,m)−n-paranormal operators,” Iraqi J. Sci., pp. 3087–3092 (2023).
[23] S. D. Mohsen, “On(n,D)-quasi operators,” Iraqi J. Comput. Sci. Math., vol. 5, no. 1, pp. 175–180 (2024).
[24] S. D. Mohsen, “Some generalizations of fuzzy soft(k∗−A)-quasinormal operators in fuzzy soft Hilbert spaces,” J. Interdiscip. Math., vol. 26, no. 6, pp. 1133–1143 (2023).
[25] E. Kreyszig, Introductory Functional Analysis with Applications. New York: Wiley (1991).
[26] V. Rakočević, “On continuity of the Moore-Penrose and Drazin inverses,” Mat. Vesn., vol. 49, pp. 163–172 (1997).
[27] K. K. Vasishtha, Teacher Education in India: A Study in New Dimensions. New Delhi: Concept Publishing (1979).
[28] C. R. Saranya and K. C. Sivakumar, “Generalized inverses of an invertible infinite matrix over a finite field,” Linear Algebra Appl., vol. 418, no. 2–3, pp. 468–479 (2006).
[29] C. Deng and A. Yu, “Some relations of projection and star order in Hilbert space,” Linear Algebra Appl., vol. 474, pp. 158–168 (2015).
[30] X. M. Xu, H. K. Du, X. Fang, and Y. Li, “The supremum of linear operators for the ∗∗-order,” Linear Algebra Appl., vol. 433, no. 11–12, pp. 2198–2207 (2010).




