On class (n, mBQ) Operators

In this paper, we introduce the class of (n, mBQ) operators acting on a complex Hilbert space H. An operator if T ∈ B (H) is said to belong to class (n, mBQ) if T ∗2mT 2n commutes with (T ∗mTn ) 2 equivalently [T ∗2mT 2n, (T ∗mTn)2] = 0, for a positive integers n and m. We investigate algebraic properties that this class enjoys. Have. We analyze the relation of this class to (n,m)-power class (Q) operators