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算子方程X^s-A~*X^(-t)A=I正算子解的范围

The range of positive operator solutions of operator equation X^s-A~*X^(-t)A=I
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摘要 利用算子理论的相关知识,在无限维的Hilbert空间上研究算子方程Xs-A*X-tA=I(s>0,t>0),得到其正算子解的范围. In this paper,the operator theory is used in the study of the operator equation Xs-A*X-tA=I(s0,t0) in infinite dimensional Hilbert space to obtain the range of its positive operator solutions.
出处 《徐州师范大学学报(自然科学版)》 CAS 2011年第1期35-36,68,共3页 Journal of Xuzhou Normal University(Natural Science Edition)
关键词 HILBERT空间 有界线性算子 正算子解 算子方程 Hilbert space bounded linear operator positive operator solution operator equation
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参考文献6

  • 1Du Shuanping, Hou Jinchuan. Positive definite solu- tions of operator equations XS-A*X-tA=I[J].Linear Multihnear Algebra,2003,51(2) :163.
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  • 3Engwerda J C, Ran A C M, Rijkeboer A L. Necessary and sufficient conditions for the existence of a positive definite solution of matrix equation XS-A*X-tA=I[J]. Linear Algebra Appl, 1993,186(6):255.
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  • 6贾艳萍,侯晋川.算子方程X^s-A~*X^(-t)A=I的正算子解[J].山西大同大学学报(自然科学版),2009,25(5):1-3. 被引量:1

二级参考文献5

  • 1Sh Du, Hou J. Positive definite solutions of operator equations X^m+A ^*X^-nA =I [J]. Linear Muhilinear Algebra, 2003, 51:163-173.
  • 2Jacob C, Engwerda. On the existence of a positive definite solution of the matrix equation X+A^TX^-1A =I [J]. Linear Algebra Appl, 1993, 194: 91-108.
  • 3Engwerda Jacob C, Andre C M Ran , Rijkeboer Arie L. Necessary and sufficient conditions for the existence of a positive definite solution of matrix equation X+A ^*X^-1A =Q [J]. Linear algebra Appl, 1993, 186: 255-275.
  • 4Liu X-G. Gao H. On the positive definite solutions of the matrix equations X^5+A ^* X^-nA =I [J]. Linear Algebra Appl, 2003, 1368: 83-97.
  • 5Zhang Y-H. On Hermitian positive definite solutions of matrix equation X+A ^*X^-2A =I [J]. Linear Algebra Appl, 2003, 372: 295-304.

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