On M-hyponormal weighted shifts ✩

Let α ≡ {αn}∞n=0 be a weight sequence and let Wα denote the associated unilateral weighted shift on 2(Z+). In this paper we prove that if α is eventually increasing, then Wα is M-hyponormal and that if α has exactly two subsequential limits such that the larger one is different from the spectral radius of Wα then Wα is not M-hyponormal.  2003 Elsevier Inc. All rights reserved