On Semi-Cubically Hyponormal Operators with First Two Equal Weights
Kyungpook Mathematicsl Journal
It is known that a semi-cubically hyponormal weighted shift need not satisfy the flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe all semi-cubically hyppnormal weighted shifts with the first two weights equal. In this paper we characterize completely the semi-cubical hyponormal shifts satisfying the additional assumption of the positive determinant coefficient property, yielding results parallel to those for quadratic hyponormality.
Exner, George R.; Baek, Seunghwan; Jung, Il Bong; and Li, Chunji. "On Semi-Cubically Hyponormal Operators with First Two Equal Weights." Kyungpook Mathematicsl Journal 56, (2016) : 899-910.