One sided x-projection, one sided x-idempotent and strongly EP elements in a ∗-ring

Abstract

In this article, we present the concept of one sided x-projection, explore and investigate left and right x-projection elements, and introduce new characterizations of one sided x-idempotent elements in a ∗-ring. We also propose numerous equivalent conditions for left x-projections within a given ring. Next, we give several equivalent conditions: Hermitian, one sided x-projection, one sided x-idempotent, and strongly EP elements in a ∗-ring.