Wanjala, VictorNyongesa, A. M.2021-05-282021-05-282021-01-122347-1557http://ijmaa.in/http://erepository.kibu.ac.ke/handle/123456789/2454In this paper, we introduce a new class of operator, the class of (α, β)-Class (Q) operator acting on a complex Hilbert space H. An operator T ∈ B(H) is said to be (α, β)-Class (Q) if α 2T∗2T 2 ≤ (T∗T) 2 ≤ β 2T ∗2T 2 for 0 ≤ α ≤ 1 ≤ β. We look at some properties that this class are privileged to enjoy.enAttribution-NonCommercial-ShareAlike 3.0 United Stateshttp://creativecommons.org/licenses/by-nc-sa/3.0/us/Class (Q)Normal(α, β)-normalHypernormal and (α, β)-Class (Q) operatorsArticle