In this paper, we consider the special case of the question raised by Halmos (see below). In particular, we show that if T k is p-hyponormal, then T is a subscalar operator of order 4k. As a corollary, we obtain that if T k is p-hyponormal and σ(T) has nonempty interior in the plane, then T has a nontrivial invariant subspace.
- Invariant subspace
- The property (β)