University of Guilan Journal of Algebra and Related Topics 2345-3931 13 1 2025 07 01 Some additive results for the g-Drazin inverse of operators 99 107 8821 10.22124/jart.2025.25909.1595 EN M. Sheibani Farzanegan Campus, Semnan University, Semnan, Iran F. Tayebi Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran N. Ashrafi Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran R. Bahmani Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran Journal Article 2023 10 31 The motivation of this article, is to establish new additive results for the g-Drazin inverse of linear operators over Banach spaces. Following the applicability of the g-Drazin inverse of operator matrices in solving the systems of linear differential equations, we then apply our results to operator matrices and obtain some results on generalized Drazin inverse of block<br />operator matrices. Drazin inverse Additive property Operator matrix Banach algebra https://jart.guilan.ac.ir/article_8821_6c3241ca8efc93feb12dd4cdcfa9f97a.pdf