几类广义Sylvester算子方程的可解性

Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1640-1652.

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Solvability of Several Kinds of Ggeneralized Sylvester Operator Equations

Xiaolin Sun,Hua Wang*()

^{College of Sciences, Inner Mongolia University of Technology, Hohhot 010051}

Received:2021-10-26 Online:2022-12-26 Published:2022-12-16
Contact: Hua Wang E-mail:hrenly@163.com
Supported by:
the NSFC(11961052);the NSF of Inner Mongolia(2022MS01005);the NSF of Inner Mongolia(2021LHMS01004);the Basic Science Research Fund in the University Directly under the Inner Mongolia Autonomous Region(JY220083);the Basic Science Research Fund in the University Directly under the Inner Mongolia Autonomous Region(JY20220151);Tenching Reform of Postgraduate Education in Inner Mongolia University of Technology(YJG2020027)

Abstract

Abstract:

In this paper, we discuss the solvability of some kinds of generalized Sylvester operator equations on Hilbert Spaces. Firstly, the necessary and sufficient conditions for the existence of solutions of AXB-XD=EB and AXB-CX = AE are given in the case of normal operators. Secondly, the solvability of three kinds of operator equations is discussed by using the uniform equivalence of operator pairs. Finally, when trigonometric operator matrix is similar to diagonal operator matrix, the corresponding operator equations are solvable.

Key words: Sylvester equation, Operator equation, Normal operator, Putnam-Fuglede's theorem

CLC Number:

O151.1

Xiaolin Sun,Hua Wang. Solvability of Several Kinds of Ggeneralized Sylvester Operator Equations[J].Acta mathematica scientia,Series A, 2022, 42(6): 1640-1652.

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References 9

1	Sylvester J . Sur l'équation en matrices px-xq. Comptes Rendus Mathematique, 1884, 99, 67- 71
2	Roth W E . The equation AX-YB=C and AX-XB=C in matrices. Proceedings of the American Mathematical Society, 1952, 3 (3): 392- 396
3	Wimmer H K . The matrix equation X - AXB = C and analogue of Roth's theorem. Linear Algebra and its Applications, 1988, 109, 145- 147 doi: 10.1016/0024-3795(88)90204-2
4	Lee S G , Vu Q P . Simultaneous solutions of matrix equations and simultaneous equivalence of matrices. Linear Algebra and its Applications, 2012, 437 (9): 2325- 2339 doi: 10.1016/j.laa.2012.06.004
5	Dmytryshyn A , Kaöm B . Coupled Sylvester-type matrix equations and block diagonalization. SIAM Journal on Matrix Analysis and Applications, 2015, 36 (2): 580- 593 doi: 10.1137/151005907
6	Eric C . The solution of the matrix equations AXB-CXD=E and (YA-DZ, YC-BZ)=(E, F). Linear Algebra and its Applications, 1987, 93 (87): 93- 105
7	Baksalary J K , Kala R . The matrix equation AXB+CYD=E. Linear Algebra and its Applications, 1980, 30 (1): 141- 147
8	Rehman A , Wang Q W , Ali I , et al. A constraint system of generalized Sylvester quaternion matrix equations. Advances in Applied Clifford Algebras, 2017, 27 (11): 3183- 3196
9	He Z H , Wang Q W , Zhang Y . A system of quaternary coupled Sylvester-type real quaternion matrix equations. Automatica, 2018, 87 (7): 25- 31

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Solvability of Several Kinds of Ggeneralized Sylvester Operator Equations

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