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has been cited by the following article:

• TITLE: Generalized Invertibility of Operators through Spectral Sets

  AUTHORS: E. Salgado-Matias, S. V. Djordjević, G. Kantún-Montiel

  KEYWORDS: Generalized Inverse, Matrix Form, Resolvent Function, Spectral Projection

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.13 No.2, February 27, 2024

  ABSTRACT: 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.