On generalized core-EP invertibility in a Banach algebra
arXiv:2309.09862
Abstract
We present new properties of generalized core-EP inverse in a Banach *-algebra. We characterize this new generalized inverse by using involved annihilators. The generalized core-EP inverse for products is obtained. The core-EP orders for Banach *-algebra elements are thereby investigated. As applications, new properties of the core-EP inverse for block complex matrices are given.
In this paper, we introduce and study a new generalized inverse in a Banach algebra with involution. Many known results on core-EP inverse are thereby extended to wider cases