ALUTHGE TRANSFORMS AND n-CONTRACTIVITY OF WEIGHTED SHIFTS

If W is a subnormal weighted shift, one might transform W in various ways: take the qth root of each weight, pick out a subsequence of weights, or take iterated Aluthge transforms of W, in each case producing another weighted shift. Via an approach to subnormality based on n-contractivity and completely monotone functions, we exhibit shifts whose transforms are again subnormal (or in related classes of interest), generalizing some recent results obtained by an approach through k-hyponormality.