Class of $\left(A,n\right)$-power-hyponormal operators \\ in semi-hilbertian space

Cherifa Chellali, benali abdelkader


In this paper, the concept of $n$-power- hyponormal operators on a hilbert space defined by Messaoud Guesba and Mostefa Nadir in $\left[10\right]$ 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 $T\in B\left(H\right)$ is $\left(A,n\right)$-power-hyponormal operator for some positive operator $A$ and for some positive integer $n$ if
$$ T^{\sharp}T^n-T^nT^{\sharp}\geq_A 0, n=1, 2, .... $$.

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