Generalized Invertibility of Operators through Spectral Sets
E. Salgado-Matias, Slaviša V. Djordjević, Gabriel Kantún-Montiel · Advances in Linear Algebra & Matrix Theory · 2023
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.