Kth roots of p-hyponormal operators are subscalar operators of order 4k

Abstract

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. © 2007 Birkhäuser Verlag Basel/Switzerland.