Analysis Seminar: "Towards a classification theory for constrained row contractions"

Abstract: Allowing for operator-valued analytic functions, it is known  that certain abstract row contractions can be classified up to unitary equivalence using concrete multiplication operators. If we are willing to settle for a less faithful description, then we may hope to construct simpler, scalar-valued functional models. For single contractions satisfying an analytic constraint, this vision has been fulfilled and has culminated in a powerful classification theorem. The aim of this talk is to investigate potential generalizations of this theorem to the multivariate world. We will highlight higher-dimensional difficulties and explain that while some of them can be circumvented, there are crucial single variable facts that simply fail to hold in several variables. Nevertheless, it is possible to obtain structural results for constrained row contractions in various special cases, such as when the zero set of the annihilating ideal forms an interpolating sequence. This is joint work in progress with Edward Timko.

Host: John McCarthy