Quadratically hyponormal weighted shifts with recursive tail
Journal of Mathematical Analysis and Applications
We characterize positive quadratic hyponormality of the weighted shift Wα(x) associated to the weight sequence α(x) : 1, 1, √ x, ( √ u, √ v, √ w)∧ with Stampfli recursive tail, and produce an interval in x with non-empty interior in the positive real line for quadratic hyponormality but not positive quadratic hyponormality for such a shift.
Exner, George R.; Jung, Il Bong; Lee, Mi Ryeong; and Park, Sun Hyun. "Quadratically hyponormal weighted shifts with recursive tail." Journal of Mathematical Analysis and Applications 408, (2013) : 298-305.