正交投影和幂等算子线性组合的W-加权Drazin逆
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摘要
借助空间分解,得到了在满足条件PQP=P时,无穷维Hilbert空间中的正交投影算子P和幂等算子Q的线性组合mP+nQ的W-加权Drazin可逆性及其W-加权Drazin逆的表达式.
Using the space decomposition,the W-weighted Drazin inverse of the linear combination of the orthogonal projection and idempotent operators is studied,and its representations in the Hilbert space are established under the condition PQP=P.
Using the space decomposition,the W-weighted Drazin inverse of the linear combination of the orthogonal projection and idempotent operators is studied,and its representations in the Hilbert space are established under the condition PQP=P.
引文
[1]Liu X J,Wu L L,Yu Y M.The group inverse of the combinations of two idempotent matrices[J].Linear and Multilinear Algebra,2011,59(1):101-115.
[2]Zhang S F,Wu J D.The Drazin inverse of the linear combinations of two idempotents in the Banach algebras[J].Linear Algebra and its Applications,2012,436(9):3132-3138.
[3]Deng C Y.The Drazin inverses of sum and difference of idempotents[J].Linear Algebra Appl,2009,430(4):1282-1291.
[4]Cvetkovic-llic D S,Deng C Y.The Drazin invertibility of the difference and the sum of two idempotent operators[J].Journal of Computation and Applied Mathematics,2010,233(8):1717-1722.
[5]Deng C Y.The Drazin inverses of products and difference of orthogonal projections[J].Journal of Mathematical Analysis and Applications,2007,335(1):64-71.
[6]Deng Y C,Wei Y M.Characterizations and representations of the Drazin inverse involving idempotents[J].Linear Algebra Appl,2009,431(9):1526-1538.
[7]段樱桃.两个幂等算子多线性组合的Drazin逆[J].信阳师范学院学报:自然科学版,2013,26(3):316-319.
[8]钟金,刘晓冀.Hilbert空间上算子W-加权Drazin逆的刻画及表示[J].数学物理学报,2010,30A(4):915-921.
[9]Drazin M P.Pseudo-inverses in associative rings and semigroups[J].Amer Math Monthly,1958,65(7):506-514.
[10]Wang G R,Wei Y M,Qiao S Z.Generalized inverses:theory and computations[M].Beijing:Science Press,2004.
[11]Wei Y M,Qiao S Z.The representation and approximation of the Drazin inverse of a linear operator in Hilbert space[J].Appl Math Comput,2003,138(1):77-89.
[12]Wang G R,Wei Y M,Qiao S Z.Generalized Inverse:Theory and Computations[M].Beijing,New York:Science Press,1993.
[13]Castro-gonzlez N,Koliha J J.New additive results for the g-Drazin inverse[J].Proc Roy Soc Edinburgh,2004,134(6):1085-1097.
[14]吴珍莺,陈剑岚,曾清平.幂等算子线性组合的Drazin可逆性[J].福建师范大学学报,2011,27(6):5-10.
[2]Zhang S F,Wu J D.The Drazin inverse of the linear combinations of two idempotents in the Banach algebras[J].Linear Algebra and its Applications,2012,436(9):3132-3138.
[3]Deng C Y.The Drazin inverses of sum and difference of idempotents[J].Linear Algebra Appl,2009,430(4):1282-1291.
[4]Cvetkovic-llic D S,Deng C Y.The Drazin invertibility of the difference and the sum of two idempotent operators[J].Journal of Computation and Applied Mathematics,2010,233(8):1717-1722.
[5]Deng C Y.The Drazin inverses of products and difference of orthogonal projections[J].Journal of Mathematical Analysis and Applications,2007,335(1):64-71.
[6]Deng Y C,Wei Y M.Characterizations and representations of the Drazin inverse involving idempotents[J].Linear Algebra Appl,2009,431(9):1526-1538.
[7]段樱桃.两个幂等算子多线性组合的Drazin逆[J].信阳师范学院学报:自然科学版,2013,26(3):316-319.
[8]钟金,刘晓冀.Hilbert空间上算子W-加权Drazin逆的刻画及表示[J].数学物理学报,2010,30A(4):915-921.
[9]Drazin M P.Pseudo-inverses in associative rings and semigroups[J].Amer Math Monthly,1958,65(7):506-514.
[10]Wang G R,Wei Y M,Qiao S Z.Generalized inverses:theory and computations[M].Beijing:Science Press,2004.
[11]Wei Y M,Qiao S Z.The representation and approximation of the Drazin inverse of a linear operator in Hilbert space[J].Appl Math Comput,2003,138(1):77-89.
[12]Wang G R,Wei Y M,Qiao S Z.Generalized Inverse:Theory and Computations[M].Beijing,New York:Science Press,1993.
[13]Castro-gonzlez N,Koliha J J.New additive results for the g-Drazin inverse[J].Proc Roy Soc Edinburgh,2004,134(6):1085-1097.
[14]吴珍莺,陈剑岚,曾清平.幂等算子线性组合的Drazin可逆性[J].福建师范大学学报,2011,27(6):5-10.