Twosetsofnewcharacterizationsfornormaland EP matrices

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

“…The following result is well known for complex matrices and for linear operators on Hilbert spaces (see [1,5,8,9]). But it is unknown for 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 normal, hyponormal and EP operators

“…In this paper we characterize normal and hyponormal operators with closed ranges, as well as EP operators on arbitrary Hilbert spaces. Using properties of operator matrices, we obtain an extension of results from [8] in infinite-dimensional settings. These characterizations are obtained using the Moore-Penrose or the group inverse of a linear bounded operator with a closed range.…”

“…Recently, S. Chen and Y. Tian (see [8]) obtained several results characterizing normal and EP complex matrices. In this paper we characterize normal and hyponormal operators with closed ranges, as well as EP operators on arbitrary Hilbert spaces.…”

Weighted partial isometries and weighted-EP elements in C*-algebras

“…Some of these results were proved for complex square matrices in [3], using the rank of a matrix, or in [1], using an elegant representation of square matrices as the main technique. Moreover, the operator analogs of these results were proved in [5,6] for linear bounded operators on Hilbert spaces, using the operator matrices as the main tool.…”