Title

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

Publication Date

2014

Journal

Journal of Operator Theory

Volume

71

Issue

2

First Page

585

Last Page

600

Abstract

We consider k-hyponormality and n-contractivity (k, n = 1, 2, . . .) as “weak subnormalities” for a Hilbert space operator. It is known that khyponormality 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.

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