Expressions for the g-Drazin inverse in a Banach algebra
Expressions for the g-Drazin inverse in a Banach algebra
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 …