Abstract:

Let T ∈ B(H) be a bounded linear operator on a complex Hilbert space H. For n ∈ N, an operator T ∈ B(H) is said to be n-normal if T nT ∗ = T ∗T n. In this paper we investigate a necessary and sufficient condition for the n-normality of ST and T S, where S, T ∈ B(H). As a consequence, we generalize Kaplansky theorem for normal operators to n-normal operators. Also, In this paper, we provide new characterizations of n-normal operators by certain conditions involving powers of Moore-Penrose inverse.

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