Journal of Operator Theory

Volume 71, Issue 2, Spring 2014 pp. 585-600.

$k$ -hyponormality and $n$ -contractivity for Agler-type shifts

Authors: Gregory T. Adams (1) and George R. Exner (2)
Author institution: (1) Department of Mathematics, Bucknell University, Lewisburg, 17837, U.S.A.
(2) Department of Mathematics, Bucknell University, Lewisburg, 17837, U.S.A.

Summary: We consider $k$ -hyponormality and $n$ -contractivity ( $k, n = 1, 2, \ldots$ ) as `weak subnormalities'' for a Hilbert space operator. It is known that $k$ -hyponormality implies $2k$ -contractivity; we produce some classes of weighted shifts including a parameter for which membership in a certain $n$ -contractive class is equivalent to $k$ -hyponormality. We consider as well some extensions of these results to operators arising as restrictions of these shifts, or from linear combinations of the Berger measures associated with the shifts.

DOI: http://dx.doi.org/10.7900/jot.2012aug08.1965
Keywords: weighted shift, subnormal operator, $n$ -contractive, $k$ -hyponormal

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