Rational dilation problems associated with constrained algebras
Functional Analysis
2018-06-29 v3 Complex Variables
Abstract
It is shown that rational dilation fails on broad collection of distinguished varieties associated to constrained subalgebras of the disk algebra of the form C + B A(D), where B is a finite Blaschke product with two or more zeros. This is accomplished in part by finding a minimal set of test functions. In addition, an Agler-Pick interpolation theorem is given and it is proved that there exist Kaijser-Varopoulos style examples of non-contractive unital representations where the generators are contractions.
Cite
@article{arxiv.1711.11090,
title = {Rational dilation problems associated with constrained algebras},
author = {Michael A. Dritschel and Batzorig Undrakh},
journal= {arXiv preprint arXiv:1711.11090},
year = {2018}
}
Comments
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