On some EP operators (Q2583092)

A bounded operator \(T\) in a Hilbert space \(H\) is said to be an \(EP\) operator if the range of \(T\) is equal to the range of its adjoint \(T^*\) and hypo-\(EP\) if it is hyponormal, i.e., the commutator \([T^*,T]\) is nonnegative. The present article gives a characterization of hypo-\(EP\) operators by means of their Moore--Penrose inverse. It is also shown that the class of hypo-\(EP\) operators is essential.