Abstract
Class (Q) operators was introduced and studied by Jibril in (quote). In this paper , we introduce and study the “cousins”
to this class, namely class (Q∗). An operator T ∈ B(H) is said to belong to class (Q∗) if T
∗2T
2 = (T T ∗)
2
. We study
the algebraic properties of this class. We also strike the relationship between this class and square hyponormal operators
through characterization of (α, β)-class (Q) operators