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

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