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.

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