On Class (BD) Operators of Order (n+k+m)

Abstract

In this paper, we introduce the class of (BD) of order (n+k+m) operators acting on the classical Hilbert space H. An operator if T ∈ B(H) is said to belong to class (BD) of order (n+k+ m)  if T ^*2(n+k+m) (T^D)² commutes with (T ^*(n+k+m)T^D)² equivalently [T ^*2(n+k+m) (T^D)², (T ^*(n+k+m)T^D)²] = 0. We investigate the properties of this class and we also analyze the relation of this class to (n+k+m)-power D-operator. The methodology involved the use of adjoint properties of these operators. Results show that the product of two doubly commuting operators is in the class of (BD) order (n+k+m) operators.