Subscalarity of -quasihyponormal operators

In this paper, we show that every ( p , k ) -quasihyponormal operator has a scalar extension and give some spectral properties of the scalar extensions of ( p , k ) -quasihyponormal operators. As a corollary, we get that such an operator with rich spectrum has a nontrivial invariant subspace. Finally, we prove that the sum of a p-hyponormal operator and an algebraic operator which are commuting is subscalar.