Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications
Functional Analysis
2020-05-18 v1
Abstract
We provide an effective single-matrix criterion, in terms of what we call the elementary Pick matrix, for the solvability of the noncommutative Nevanlinna-Pick interpolation problem in the row ball, and provide some applications. In particular we show that the so-called "column-row property" fails for the free semigroup algebras, in stark contrast to the analogous commutative case. Additional applications of the elementary Pick matrix include a local dilation theorem for matrix row contractions and interpolating sequences in the noncommutative setting. Finally we present some numerical results related to the failure of the column-row property.
Cite
@article{arxiv.2005.07556,
title = {Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications},
author = {Meric Augat and Michael T. Jury and James Eldred Pascoe},
journal= {arXiv preprint arXiv:2005.07556},
year = {2020}
}
Comments
21 pages