Left and right generalized Drazin invertible operators on Banach spaces and applications

[EN] In this paper, left and right generalized Drazin invertible operators on Banach spaces are defined and characterized by means of the generalized Kato decomposition. Then, new binary relations associated with these operators are presented and studied. In addition, a new characterization of the generalized Drazin pre-order and a sufficient condition for that to be a partial order are given by using a matrix operator technique.This paper was partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria (grant Resol. No 155/14), Universidad Nacional de Rio Cuarto (grant PPI 18/C472) and CONICET (grant PIP 112-201501-00433CO). Fourth author was partially supported by Ministerio de Economia y Competitividad of Spain (grant Red de Excelencia MTM2017-90682-REDT).Ferreyra, DE.; Latanzi, M.; Levis, F.; Thome, N. (2019). Left and right generalized Drazin invertible operators on Banach spaces and applications. Operators and Matrices. 13(3):569-583. https://doi.org/10.7153/oam-2019-13-43S56958313

Weighted G-Drazin inverses and a new pre-order on rectangular matrices

[EN] This paper deals with weighted G-Drazin inverses, which is a new class of matrices introduced to extend (to the rectangular case) G-Drazin inverses recently considered by Wang and Liu for square matrices. First, we define and characterize weighted G-Drazin inverses. Next, we consider a new pre-order defined on complex rectangular matrices based on weighted G-Drazin inverses. Finally, we characterize this pre-order and relate it to the minus partial order and to the weighted Drazin pre-order. (C) 2017 Elsevier Inc. All rights reserved.This paper was partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria, grant resol. no. 155/14. The first and third authors were partially supported by Ministerio de Economia y Competitividad of Spain (grant no. DGI MTM2013-43678-P) and the third author was also partially supported by Ministerio de Economia y Competitividad of Spain (Red de Excelencia MTM2015-68805-REDT).Coll, C.; Lattanzi, M.; Thome, N. (2018). Weighted G-Drazin inverses and a new pre-order on rectangular matrices. Applied Mathematics and Computation. 317:12-24. https://doi.org/10.1016/j.amc.2017.08.047S122431