Factorizations of EP operators

Abstract

In this paper we characterize EP operators through the existence of different types of factorizations. Our results extend to EP operators existing characterizations for EP matrices and give new characterizations both for EP matrices and EP operators.2000 Mathematics Subject Classification. Primary 47A05, 15A09; Secondary 47B.

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

“…Introduction. 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.…”

Characterizations of *-DMP matrices over rings

“…In [3,4,7,16], the authors gave some characterizations of real or complex EP matrices, EP Hilbert operators, EP Banach algebra elements, and weighted EP Banach space operators through factorizations respectively.…”

EP matrices: computation of the Moore-Penrose inverse via factorizations

“…In a recent paper of Drivaliaris, Karanasios and Pappas [3], the following theorem was given, for operators acting on a infinite dimensional complex Hilbert space H:…”

“…Pearl again [8], showed that a matrix A is EP if and only if there exists an invertible matrix V such that A * = V A. On a recent paper for operators acting on Hilbert spaces, Drivaliaris, Karanasios and Pappas [3] gave a similar factorization result of the form T † = V T , where T is an EP operator and V is invertible. Following these results, we give two factorization algorithms that will be used for the computation of the generalized inverse matrix.…”