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.
- (p,k)-Quasihyponormal operator
- Algebraic operator
- Invariant subspace
- P-Hyponormal operator
- Subscalar operator