# 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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