Journal of Operator Theory

Volume 61, Issue 2, Spring 2009 pp. 419-438.

Aluthge transforms and $n$-contractivity of weighted shifts

Authors: George R. Exner
Author institution: Department of Mathematics, Bucknell University, Lewisburg, PA, 44691, USA

Summary: If $W$ is a subnormal weighted shift, one might transform $W$ in various ways: take the $q$th 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.

Keywords: Weighted shifts, subnormal operators, completely hyperexpansive, $n$% -contractive, $k$-hyponormal.

Contents Full-Text PDF