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We prove some further properties of the operator ∈[QN](-power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator∈[QN] satisfying the translation invariant property is normal and that theoperator ∈[QN] is not supercyclic provided that it is not invertible. Also, westudy some cases in which an operator ∈[2QN] is subscalar of order ; that is, it issimilar to the restriction of a scalar operator of order  to an invariant subspace

On Some Normality-Like Properties and Bishop's Property () for a Class of Operators on Hilbert Spaces