George R. Exner

Criteria for positively quadratically hyponormal weighted shifts

For bounded linear operators on Hilbert space, positive quadratic hyponormality is a property strictly between subnormality and hyponormality and which is of use in exploring the gap between these more familiar properties. Recently several related positively quadratically hyponormal weighted shifts have been constructed. In this note we establish general criteria for the positive quadratic hyponormality of weighted shifts which easily yield the results for these examples and other such weighted shifts.

Berger Measure for Some Transformations of Subnormal Weighted Shifts

A subnormal weighted shift may be transformed to another shift in various ways, such as taking the p-th power of each weight or forming the Aluthge transform. We determine in a number of cases whether the resulting shift is subnormal, and, if it is, find a concrete representation of the associated Berger measure, directly for finitely atomic measures, and using both Laplace transform and Fourier transform methods for more complicated measures. Alternatively, the problem may be viewed in purely measure-theoretic terms as the attempt to solve moment matching equations such as

Some Multplicities for Contractions with Hilbert-Schmidt Defect

{(\int t^n \, d\mu(t))^2 = \int t^n \, d\nu(t)}

Semi-cubic Hyponormality of Weighted Shifts with Stampfli Recursive Tail

(∫tndμ(t))2=∫tndν(t) (

DILATIONS FOR POLYNOMIALLY BOUNDED OPERATORS

{n=0, 1, \ldots}

Weakly n-hyponormal Weighted Shifts and Their Examples

n=0,1,…) for one measure given the other.