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算子方程AXB^*-BX^*A^*=C的解

Solutions to the operator equation AXB~*-BX~*A~*=C
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摘要 设A∈B(H3,H2),B∈B(H1,H2),其中Hi,i=1,2,3都表示Hilbert空间。本文利用算子分块的技巧,在算子A,B值域闭以及R(B)R(A)的条件下讨论了算子方程AXB*-BX*A*=C解存在的充要条件并用算子矩阵的形式给出了一般解的表示形式。特别地,讨论了当B是一个正交投影算子P时,算子方程AXP-PX*A*=C的解存在的充要条件以及一般解的表示。 A∈B(H3,H2),B∈B(H1,H2),while Hi(i=1,2,3) are Hilbert spaces.Using of the technique of block operator matrix,when the range of A is closed and R(B)■R(A),the sufficient and necessary conditions for the existence of solutions to the operator equation AXB*-BX*A*=C and the representation of solutions are established.Especially,when B is an orthogonal projection P,the sufficient and necessary conditions for the existence of solutions to the operator equation AXP-PX*A*=C and the representation of solutions are also given.
作者 许俊莲
出处 《山东大学学报(理学版)》 CAS CSCD 北大核心 2012年第4期47-52,共6页 Journal of Shandong University(Natural Science)
基金 陕西省宝鸡文理学院院级重点科研项目(ZK11132)
关键词 算子方程 MOORE-PENROSE逆 算子矩阵 正交投影 operator equation Moore-Penrose inverse operator matrix orthogonal projection
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  • 1袁永新.关于一类线性矩阵方程的对称解[J].工程数学学报,1998,15(3):25-29. 被引量:34
  • 2ARONSZAJN N, SMITH K T. Invariant subspaces of completely continuous operators [J]. Annals of Mathematics, 1954, 60: 345-350.
  • 3HOLBRLLK J, NORDREN F, RADJARI H, et al. On the operator equation AX = XAX I-J]. Linear Algebra and its Applications, 1999, 295 113-116.
  • 4CONWAY J B. A Course in Functional Analysis [M]. New York: Springer-Verlag, 1990.
  • 5CLINE R E. Representations for the generalized inverse of a partitioned matrix[J], Journal of the Society for Industrial and Applied Mathematics, 1964, 12: 588-600.
  • 6KOLIHA J J, RAKOCEVIC V, STRASKRABA I. The difference and sum of projectors[J]. Linear Algebra and its Applications, 2004, 388: 279-288.
  • 7GROB J. On the product of orthogonal projectors [J].Linear Algebra and its Applications, 1999, 289: 141-150.
  • 8KOLIHA J J, RAKOCEVIC V, STRASKRABA I. Fredholm properties of the difference of orthogonal projection in a Hilbert space[J]. Integral Equations and Operator Theory, 2005, 52 : 125-134.
  • 9CONWAY J B. A Course in functional analysis[ M]. New York: Springer-Verlag, 1990.
  • 10SCHUR I. Potenzreihn in innern des heitskreises[J]. Journal ftir die reine und angewandte Mathematik, 1917, 147: 205-232.

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