Generalized Invertibility of Operators through Spectral Sets  

作　　者：E. Salgado-Matias S. V. Djordjević G. Kantún-Montiel E. Salgado-Matias;S. V. Djordjević;G. Kantún-Montiel(Facultad de Ciencias Fí,sico Matemá,ticas, Benemé,rita Universidad Autó,noma de Puebla, Puebla, Mexico)

机构地区：[1]Facultad de Ciencias Fí,sico Matemá,ticas, Benemé,rita Universidad Autó,noma de Puebla, Puebla, Mexico

出　　处：《Advances in Linear Algebra & Matrix Theory》2023年第2期21-35,共15页线性代数与矩阵理论研究进展（英文）

摘　　要：If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.

关 键 词：Generalized Inverse Matrix Form Resolvent Function Spectral Projection 

分 类 号：O17[理学—数学]