The class of (n,m)power-A-quasi-hyponormal operators in semi-Hilbertian space

Abstract

The concept of K-quasi-hyponormal operators on semi-Hilbertian space is defined by Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali in [7]. This paper is devoted to the study of new class of operators on semi-Hilbertian space H, ∥_. ∥_Acalled (n,m)power-A-quasi-hyponormal denoted [(n,m)QH]_A.We give some basic properties of these operators and some examples are also given .An operator T ∈ B_A(H) is said to be (n,m) power-A-quasi-hyponormal for some positive operator A and for some positive integers n and m if T^⋕((T^⋕)^mTⁿ— Tⁿ(T^⋕)^m)T≥_A or equivalently AT^⋕((T^⋕)^mTⁿ— Tⁿ(T^⋕)^m)T≥0