**Date & Time:** Tuesday, November 8, 2011, 15:00-16:00

**Venue:** Ramanujan Hall

**Title:** n-contractivity and k-hyponormality

**Speaker:** Prof. George Exner, Bucknell University, USA

**Abstract:** The subnormality of a Hilbert space operator has two
standard characterizations, one due to Bram-Halmos and the
other to Agler-Embry. These characterizations naturally give
rise to the classes of k-hyponormal (k=1, 2, ...) and
n-contractive (n=1, 2, ...) operators respectively.

While relationships between the two collections of classes are not well understood, we consider some of the history of results in this area and exhibit some families of perturbations of subnormal weighted shift operators (such as perturbations of the Bergman shift) for which the relationship is unexpectedly strong.