# 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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