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

Abdelkader Benali


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 if

Tn+ T#n A 0, n = 1,2,...

Keywords: Real power, Semi-Hilbertian space, Semi-inner product, Positive operators. 2000

Mathematics Subject Classification: Primary 47B20. Secondary 47B99

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