On the class of (A,n) - real power positive operators in semi-hilbertian space

In this paper, the concept of the class of n-Real power positive operators on a hilbert space defined by Abdelkader Benali in [1] 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) - Real power positive operators for some positive operator A and for some positive integer n ifTn + T#n ≥A 0, n = 1,2,...Keywords: Real power, Semi-Hilbertian space, Semi-inner product, Positive operators. 2000Mathematics Subject Classification: Primary 47B20. Secondary 47B99