Solvability of an Unbounded Operator Equation


  • Karrar Mohammed Kadhim Ministry of Education, Maysan, Iraq



Operator Equations, Semigroup, Unbounded Operator, Generalized Semigroup


In this work, we will submit the form of the solution of the generalization kind of unbounded operator equation define on Hilbert space which is , where  is the bounded operator satisfy the above operator equations and showing this solution via application the semigroup theory, moreover we will discuss some properties of this solution and proved its unique. Also, it was proved that for a locally bounded operator  satisfying the equation.


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V. S. Belonosov, “INSTABILITY INDICES OF DIFFERENTIAL OPERATORS,” Mathematics of the USSR-Sbornik, vol. 57, no. 2, pp. 507–525, Feb. 1987, doi: 10.1070/SM1987v057n02ABEH003083.

T. Nambu, “Feedback stabilization of diffusion equations by a functional observer,” J Differ Equ, vol. 43, no. 2, pp. 257–280, Feb. 1982, doi: 10.1016/0022-0396(82)90094-8.

M. Rosenblum, “The Operator Equation BX - XA = Q with Selfadjoint A and B,” Proceedings of the American Mathematical Society, vol. 20, no. 1, p. 115, Jan. 1969, doi: 10.2307/2035971.

V. Q. Phóng, “The operator equation AX - XB = C with unbounded operators A and B and related abstract Cauchy problems.,” Mathematische Zeitschrift, vol. 208, no. 4, pp. 567–588, 1991, [Online]. Available:

S. Schweiker, “Mild solutions of second-order differential equations on the line,” in Mathematical Proceedings of the Cambridge Philosophical Society, 2000, vol. 129, no. 1, pp. 129–151. doi: 10.1017/S0305004199004351.

N. T. Lan, “ On the operator equation A X−X B=C with unbounded operators A,B , and C ,” in Abstract and Applied Analysis, 2001, vol. 6, no. 6, pp. 317–328. doi: 10.1155/s1085337501000665.

N. A. Caruso and A. Michelangeli, “Krylov Solvability of Unbounded Inverse Linear Problems,” Integral Equations and Operator Theory, vol. 93, no. 1, p. 1, Feb. 2021, doi: 10.1007/s00020-020-02616-2.

E. Kreyszig, Introductory functional analysis with applications, vol. 17. John Wiley & Sons, 1991.

A. Pazy, Semigroups of linear operators and applications to partial differential equations, vol. 44. Springer Science & Business Media, 2012.




How to Cite

Mohammed Kadhim, K. (2024). Solvability of an Unbounded Operator Equation. Journal of Al-Qadisiyah for Computer Science and Mathematics, 16(2), Math. 56–61.



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