EP elements in rings

On EP elements, normal elements and partial isometries in rings with involution

“…EP matrices and normal matrices, as well as EP linear operators and normal linear operators on Banach or Hilbert spaces have been investigated by many authors (see, for example, [1,2,3,4,5,7,8,9,10,11,13,15,17,18,20]). D. Mosić et al in [21,24] use the setting of rings with involution to investigate EP elements and normal elements, giving new characterizations to them and providing simpler and more transparent proofs to already existing ones. D. Mosić and D.S.…”

Group, Moore–Penrose, core and dual core inverse in rings with involution

“…Namely, x = q * aq. The analogous property can be shown for all corner elements in (11). The proof is left to the reader.…”

“…Recently, the EP elements are investigated in the context of rings with involution. For a recent account of the theory see, for example, [5], [11] and the references given there. (ii) a ∈ R † and p a = r a .…”

“…The elements in upper left corners in (11) belong to the sets of the forms p 1 Rp 2 , where p 1 and p 2 are idempotents. When p 1 = p 2 we can not consider the invertibility of the corner element in p 1 Rp 2 , but it has some similar property.…”

EP Elements in Rings with Involution

“…Also, they showed that R † ∩ R # = R † ∩ R # . Motivated by [4,8,10,11], in this paper, we will give new equivalent characterizations such that an element in R to be an EP element.…”