On (α,β)-Class (Q) Operators

Abstract

In 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.