On Class (Q )

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