On Semi-weakly n-Hyponormal Weighted Shifts
Integral Equations and Operator Theory
Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved that there exists a semi-weakly three-hyponormal weighted shift W (alpha) with alpha (0) = alpha (1) < alpha (2) which is not two-hyponormal, which illustrates the gaps between various weak subnormalities.
Do, Younghae; Exner, George; Jung, Il Bong; and Li, Chungji. "On Semi-weakly n-Hyponormal Weighted Shifts." Integral Equations and Operator Theory (2012) : 93-106.