无限维Hilbert空间上一类算子方程的解
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摘要
本文运用幂等算子A在空间分解下的矩阵形式与其Moore-Penrose广义逆A+,研究了一类算子方程XA-A*X=B的解和自伴解的充分必要条件,并给出了算子方程XA-A*X=B的解和自伴解的一般结构.
In this Infinite Dimensional Hilbert Space,when A is an idempotent operator,we give the sufficient and necessary conditions for the existence of solutions of the equation XA-A*X = B and the representations of those solutions,Using the block operator matrix technique and Moore-Penorose inverse of operator A+.
In this Infinite Dimensional Hilbert Space,when A is an idempotent operator,we give the sufficient and necessary conditions for the existence of solutions of the equation XA-A*X = B and the representations of those solutions,Using the block operator matrix technique and Moore-Penorose inverse of operator A+.
引文
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[2]Sorensen D C,Antoulas A C.The Sylvester equation and approximate balanced reduction[J].Linear Algebra Appl,2002,351:671~700.
[3]Djordjevic D S.Explicit solution of the operator equation[J].Journal of Computational and Applied Mathmatics,2007,200(2):701~704.
[4]徐俊莲,杜鸿科.算子方程AXA*=B的解[J].西安文理学院学报(自然科学版),2008,11(2):7~9.
[5]DU H K,YAO X Y,DENG C Y.Invertibility of linear combinations of two idempotents[J].Proceedings of the American Mathematical Society,2005,134(5):1451~1457.