Partial isometries and EP elements in rings with involution

Abstract

If R is a ring with involution, and a^† is the Moore-Penrose inverse of a ∈ R, then
the element a is called: EP, if aa^† = a^†a; partial isometry, if a^∗ = a^†; star-dagger, if a^∗a^† = a^†a^∗. In this paper, characterizations of partial isometries, EP elements and star-dagger elements in rings with involution are given. Thus, some well-known results are extended to more general settings.