Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality
Integral Equations and Operator Theory
Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.
Exner, George; Jung, Il Bong; Lee, Mi Ryeong; and Park, Sun Hyun. "Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality." Integral Equations and Operator Theory 79, no. 1 (2014) : 49-66.