Let ܪ be a Hilbert space and let ܣ be a positive bounded operator on .ܪ The Semi Inner Product ⟨ߦ│ߟ⟩ ∶= ⟨ߦ│ߟ⟩ , ξ ,η∈ ܪ induces a Semi norm ‖. ‖ on .ܪ This makes ܪ into a Semi-Hilbertian Space. In this Manuscript we introduce the Generalization of Normal Operator named as (݊, ݉)-power quasi normal operators [6] in Semi-Hilbertian Space ,ܪ( ‖. ‖) with the help of the papers like positive normal, -ܣ normal, -ܣquasi normal, ,ܣ( ݊)-power quasi normal and also isometries in the same space. Now we generalize the above papers and named it as (݊, ݉)-power quasi normal operators in semi-hilbertian spaces.
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