Let X, Y be reflexive strictly convex Banach spaces, let T, δT ： X → Y be bounded linear operators with closed range R（T）. Put T= T ＋ δT. In this paper, by using the concept of quasiadditivity and the so called...Let X, Y be reflexive strictly convex Banach spaces, let T, δT ： X → Y be bounded linear operators with closed range R（T）. Put T= T ＋ δT. In this paper, by using the concept of quasiadditivity and the so called generalized Neumman lemma, we will give some error estimates of the bounds of ｜｜T^M｜｜. By using a relation between the concepts of the reduced minimum module and the gap of two subspaces, some new existence characterization of the Moore-Penrose metric generalized inverse T^M of the perturbed operator T will be also given.展开更多
基金supported by China Postdoctoral Science Foundation(Grant No.2015M582186)He’nan Institute of Science and Technology Postdoctoral Science Foundation(Grant No.5201029470209)
文摘Let X, Y be reflexive strictly convex Banach spaces, let T, δT ： X → Y be bounded linear operators with closed range R（T）. Put T= T ＋ δT. In this paper, by using the concept of quasiadditivity and the so called generalized Neumman lemma, we will give some error estimates of the bounds of ｜｜T^M｜｜. By using a relation between the concepts of the reduced minimum module and the gap of two subspaces, some new existence characterization of the Moore-Penrose metric generalized inverse T^M of the perturbed operator T will be also given.
基金The research was supported by the Science Rreasch Grant (10553024) of Education Department of Heilongjiang Province and NSF Grant (10471032) of China
