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

Abstract

s of KOTAC Volume 10(2008), 10–10 k-hyponormality and n-contractivity for Agler-type shifts George Exner Bucknell University, Lewisburg, PA 17837, USA exner@bucknell.edu The well-known Bran-Halmos condition for subnormality of Hilbert space operators gives rise to the classes of k-hyponormal operators, k = 1, 2, · · · . The Agler-Embry condition for subnormality of a contraction uses the n-contractive classes, n =, 1, 2, · · · . The comparative study of these classes has been fruitful: for example, if a contraction is khyponormal it is 2k-contractive. We consider some back-step extensions of Agler model weighted shifts for which an n-contractivity condition guarantees (in some cases, is equivalent to) a k-hyponormality one. Elements of the study include the Berger measure of a subnormal shift and orthogonal polynomials.