%0 Journal Article
%T Generalized Invertibility of Operators through Spectral Sets
%A E. Salgado-Matias
%A S. V. Djordjevi£¿
%A G. Kantš²n-Montiel
%J Advances in Linear Algebra & Matrix Theory
%P 21-35
%@ 2165-3348
%D 2023
%I Scientific Research Publishing
%R 10.4236/alamt.2023.132002
%X 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 <i>n</i> of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.
%K Generalized Inverse
%K Matrix Form
%K Resolvent Function
%K Spectral Projection
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=131383