arXiv subjects
Publications and source records attributed to Greg Knese.
An abstract Pick interpolation theorem for a family of positive semi-definite kernels on a set $X$ is formulated. The result complements those in \cite{Ag} and \cite{AMbook} and will subsequently be applied to Pick interpolation on distinguished varieties \cite{JKM}.
We consider pairs of commuting isometries that are annihilated by a polynomial. We show that the polynomial must be inner toral, which is a geometric condition on its zero set. We show that cyclic pairs of commuting isometries are nearly unitarily equivalent if they are annihilated by the same minimal polynomial.