Dilations and constrained algebras
Abstract
It is well known that unital contractive representations of the disk algebra are completely contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f whose first derivative vanishes at 0. We prove that there are unital contractive representations of A which are not completely contractive, and furthermore provide a Kaiser and Varopoulos inspired example for A and present a characterization of those contractive representations of A which are completely contractive. In the positive direction, for the algebra of rational functions with poles off the distinguished variety V in the bidisk determined by (z-w)(z+w)=0, unital contractive representations are completely contractive.
Cite
@article{arxiv.1305.4272,
title = {Dilations and constrained algebras},
author = {Michael A. Dritschel and Michael T. Jury and Scott McCullough},
journal= {arXiv preprint arXiv:1305.4272},
year = {2013}
}
Comments
New to version 2 is a proof of rational dilation for the distinguished variety in the bidisk determined by (z-w)(z+w)=0