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In this paper, the concept of n-power quasi-normal operators on a Hilbert space defined by Sid Ahmed in (14) is generalized when an additional semi-inner product is considered. This new concept is described by means of oblique projections. For a Hilbert space operator T ∈ B(H) is (A,n)-power quasi-normal operators for some positive operator A and for some positive in- teger n if ,

CLASS OF (A,n)-POWER QUASI-NORMAL OPERATORS IN SEMI-HILBERTIAN SPACES