(n, m) Power-(D, A)-Hyponormal Operators in Semi-Hilbertian Space

Abstract

In this paper we introduce and analyze a new class of operators on semi- Hilbertian space (H, .  _A) called (n, m) power-(D, A)-hyponormal denoted [(n, m)DH]A associated with a Drazin invertible operator using its Drazin inverse. After es- tablishing the basic properties of such operators and some examples are also

given. We show some results related to this class on semi-Hilbertian space. In addition, we characterize the direct sum and the tensor product of these operators. An operator T ∈ B_A(H)^D is (n, m) power-(D, A)-hyponormal for some positive operator A and for some positive integers n and m if

(T^♯)^m(T^D)ⁿ − (T^D)ⁿ(T^♯)^m ≥_A 0