  The purpose of this paper is to explore additional properties of left Drazin
invertible, essentially left Drazin invertible, right Drazin invertible, and
essentially right Drazin invertible operators on Banach spaces, building upon
the groundwork laid in [8] and [19]. Specifically, we propose alternative
definitions for these operators and investigate their behavior in powers.
Furthermore, we employ a specific operator decomposition to characterize these
operators, providing a deeper understanding of their structure and properties.
The operators we study are distinguished from other operators bearing the same
name in existing literature, see [1], [9]. By employing more refined
definitions, we uncover a broader range of properties for these operators,
setting them apart from their counterparts in the literature.
