Affiliation:
1. Department of Mathematics, Hangzhou Normal University, Hangzhou, China
2. Women’s University of Semnan (Farzanegan), Semnan, Iran
Abstract
We explore the generalized Drazin inverse in a Banach algebra. Let A be a
Banach algebra, and let a,b ? Ad. If ab = ?a?bab? for a nonzero complex
number ?, then a + b ? Ad. The explicit representation of (a + b)d is
presented. As applications of our results, we present new representations
for the generalized Drazin inverse of a block matrix in a Banach algebra.
The main results of Liu and Qin [Representations for the generalized Drazin
inverse of the sum in a Banach algebra and its application for some operator
matrices, Sci. World J., 2015, 156934.8] are extended.
Publisher
National Library of Serbia