On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces

En este trabajo se estudia la perturbación de la inversa generalizada grupo en el ámbito de los operadores lineales y acotados sobre un espacio de Banach complejo. Se establecen, en primer lugar, caracterizaciones de los {1,2}-inversos generalizados de operadores perturbados que verifican una condición de no singularidad. Posteriormente se caracteriza la clase de operadores perturbados para los cuales existe el operador inverso grupo y verifican ciertas condiciones geométricas. Se prueba que los operadores perturbados tienen una determinada estructura de matriz 2 por 2 de operadores y se desarrolla una representación para la resolvente de tales matrices de operadores a partir de la cual se obtiene una representación para el operador inverso grupo. Este resultado extiende al contexto de operadores un resultado para matrices por bloques incluido en el libro [Campbell y Meyer, Generalized inverses of Linear Transformations, Dover, 1979] y nos proporciona una herramienta para el análisis de la perturbación. Otras aportaciones son la obtención de xpresiones explícitas para el operador inverso grupo el operador perturbado y su proyección espectral asociada al 0 y la obtención de cotas superiores para el error relativo de la inversa de Drazin y de los proyectores espectrales y un resultado de continuidad de la inversa grupo para operadores en espacios de Banach. Las aportaciones de este trabajo extienden o complementan resultados obtenidos previamente por autores sobre el mismo tema (Djordjevic, Koliha, Rakoèevic) Given a bounded operator A on a Banach space X with Drazin inverse AD and index r, we study the class of group invertible bounded operators B such that I + A(D)(B - A) is invertible and R(B) boolean AND N(A(r)) = {0}. We show that they can be written with respect to the decomposition X = R(A(r))circle plus N(A(r)) as a matrix operator, B = (B-1 B-12 B-21 B21B1-1B12), where B-1 and B-1(2) + B12B21 are invertible. Several characterizations of the perturbed operators are established, extending matrix results. We analyze the perturbation of the Drazin inverse and we provide explicit upper bounds of parallel to B-# - A(D)parallel to and parallel to BB# - A(D)A parallel to. We obtain a result on the continuity of the group inverse for operators on Banach space

The star partial order and the eigenprojection at 0 on EP matrices

[EN] The space of n x n complex matrices with the star partial order is considered in the first part of this paper. The class of EP matrices is analyzed and several properties related to this order are given. In addition, some information about predecessors and successors of a given EP matrix is obtained. The second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders. 2012 Elsevier Inc. All rights reserved.This paper was partially supported by Ministry of Education of Argentina (PPUA, Grant Resol. 228, SPU, 14-15-222) and by Universidad Nacional de La Pampa, Facultad de Ingenieria (Grant Resol. No 049/11).Hernández, AE.; Lattanzi, MB.; Thome, N.; Urquiza, F. (2012). The star partial order and the eigenprojection at 0 on EP matrices. Applied Mathematics and Computation. 218(21):10669-10678. https://doi.org/10.1016/J.AMC.2012.04.034S10669106782182

Error Bounds for the Perturbation of the Drazin Inverse of Closed Operations with Equal Spectral Projections

We study perturbations of the Drazin inverse of a closed linear operator A for the case when the perturbed operator has the same spectral projection as A. This theory subsumes results recently obtained by Wei and Wang, Rakočevič and Wei, and Castro and Koliha. We give explicit error estimates for the perturbation of Drazin inverse, and error estimates involving higher powers of the operators

Resolution 89-6-F - Food Services Committee

Resolution to create a student advisory food services committee

Continuity and general perturbation of the Drazin inverse for closed linear operators

We study perturbations and continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and the gap between ranges and nullspaces of operators. The results are used to derive a theorem on the continuity of the Drazin inverse for closed operators and to describe the asymptotic behavior of operator semigroups

in the open right halfplane, then the inverse of A can be represented by

Abstract. In this note we present an integral representation for the Drazin inverse AD of a complex square matrix A. This representation does not require any restriction on its eigenvalues. Key words. Drazin inverse, Integral representation