# Solvability of Sylvester operator equation with bounded subnormal operators in Hilbert spaces

## Main Article Content

## Abstract

## Article Details

## Supporting Agencies

## References

[1] R. Bhatia, Matrix Analysis, Graduate Texts in Mathematics, Vol. 169, Springer- Verlag, New York, 1997. Google Scholar

[2] R. Bhatia and P. Rosental, How and why to solve the operator equation AX − XB = Y , Bull. London. Math. Soc. 29 (1997), 1–21. Google Scholar

[3] J. B. Conway, The theory of subnormal operators, Math. Surveys and Mon- graphs, Vol. 36, Amer. Math. Soc. Providence Rhode Island, 1991. Google Scholar

[4] D. S. Dlordjevi c, Explicit solution of the operator equation A*X + X*A = B, J. Comp. Appl. Maths 200 (2007), 701-704. Google Scholar

[5] T. Furuta, On relaxation of normality in the Fuglede-Putnam theorem, Proc. Amer. Math. Soc. 77 (3) (1979), 324–328. Google Scholar

[6] J. D. Gardiner, A. L. Laub, J. J. Amato, and C. B. Moler, Solution of the Sylvester matrix equation AXB + CXD = E, ACM Trans. Math. Software 18 (2) (1982), 223–231. Google Scholar

[7] A. Jameson, Solutions of equation AX − XB = C by inversion of M × M or N × N matrices, SIAM J. Appl. Math. 16 (1968), 1020–1023. Google Scholar

[8] P. Lancaster and M. Tismenetsky, The Theory of Matrices with Applications, second edition. Academic Press, New York, (1985). Google Scholar

[9] A. Mansour, L. Hariz and H. Gaaya, A priori estimate for the solution of sylvester equation, J. Adv. Maths. 10 (7) (2015), 3633–3638. Google Scholar

[10] S. Mecheri and A. Mansour, On the operator equation AXB − XD = E, Lobachevskii. J. Math. 30 (NTA3), 224 (2009). Google Scholar

[11] M. Resenblum, On a theorem of Fuglede and Putnam, J. Lond. Math. Soc. 33 (1958), 376–377. Google Scholar

[12] M. Resenblum, On the operator equation AX − X B = Q with self-adjoint A and B, Proc. Amer. Math. Soc. 20 (1969), 115–120. Google Scholar

[13] W. E. Roth, The equation AX −Y B = C and AX −XB = C in matrices, Proc. Amer. Math. Soc. 3 (1952), 392–396. Google Scholar

[14] A. Schweinsberg, The operator equation AX − XB = C with normal A and B, Pacific J. Math. 102 (2) (1982). Google Scholar

[15] M. Sang Lee, A note on the subnormal operators, Commun. Korean Math. Soc. 3 (1) (1988), 51–58. Google Scholar