Interpolation in Semigroupoid Algebras
Functional Analysis
2007-05-23 v3 Operator Algebras
Abstract
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a family of test functions over a broad class of semigroupoids. There is then an associated interpolation theorem. Besides leading to solutions of the familiar Nevanlinna-Pick and Caratheodory-Fejer interpolation problems and their multivariable commutative and noncommutative generalizations, this approach also covers more exotic examples.
Cite
@article{arxiv.math/0507083,
title = {Interpolation in Semigroupoid Algebras},
author = {Michael A. Dritschel and Stefania Marcantognini and Scott McCullough},
journal= {arXiv preprint arXiv:math/0507083},
year = {2007}
}
Comments
33 pages. Updated references and corrected typos. To appear in Journal fur die reine und angewandte Mathematik