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arXiv · 1305.4272

Dilations and constrained algebras

Michael A. Dritschel·Michael T. Jury·Scott McCullough
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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.

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Michael A. Dritschel, Michael T. Jury, Scott McCullough. 2013-10-17. Dilations and constrained algebras. https://arxiv.org/abs/1305.4272

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