Given two closed, in general unbounded, operators A and C, we investigate the left invertible completion of the partial operator matrix A ？ 0 C. Based on the space decomposition technique, the alternative sufficient ...Given two closed, in general unbounded, operators A and C, we investigate the left invertible completion of the partial operator matrix A ？ 0 C. Based on the space decomposition technique, the alternative sufficient and necessary conditions are given according to whether the dimension of R（A）⊥ is finite or infinite.As a direct consequence, the perturbation of left spectra is further presented.展开更多
基金partially supported by the Natural Science Foundation of China(Nos.11461049 and 11371185)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20111501110001)+3 种基金the ‘Chunhui Program’ of the Ministry of Education of China(No.Z2009-1-01010)the Major Program of the National Natural Science Foundation of Inner Mongolia(No.2013ZD01)the National Science Foundation for Fostering Distinguished Young Scholars of Inner Mongolia(No.2013JQ01)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia(No.NJYT-12-B06)
文摘Given two closed, in general unbounded, operators A and C, we investigate the left invertible completion of the partial operator matrix A ？ 0 C. Based on the space decomposition technique, the alternative sufficient and necessary conditions are given according to whether the dimension of R（A）⊥ is finite or infinite.As a direct consequence, the perturbation of left spectra is further presented.
