Wanjala, VictorNyongesa, A. M.2021-07-012021-07-012020-11-12http://erepository.kibu.ac.ke/handle/123456789/2482Class (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) operatorsenAttribution-NonCommercial-ShareAlike 3.0 United Stateshttp://creativecommons.org/licenses/by-nc-sa/3.0/us/Normal operators, Square-hyponormal operators, Class (Q) operators, Almost Class (Q), Class (Q∗) operators.Article