Distinguished Varieties
Functional Analysis
2007-05-23 v1 Complex Variables
Abstract
A distinguished variety is a variety that exits the bidisk through the distinguished boundary. We show that Ando's inequality for commuting matrix contractions can be sharpened to looking at the maximum modulus on a distinguished variety, not the whole bidisk. We show that uniqueness sets for extremal Pick problems on the bidisk always contain a distinguished variety.
Cite
@article{arxiv.math/0504084,
title = {Distinguished Varieties},
author = {Jim Agler and John McCarthy},
journal= {arXiv preprint arXiv:math/0504084},
year = {2007}
}