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Lookup NU author(s): Dr Michael DritschelORCiD
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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.
Author(s): Dritschel MA, Jury MT, McCullough S
Publication type: Article
Publication status: Published
Journal: Operators and Matrices
Year: 2016
Volume: 10
Issue: 4
Pages: 829-861
Print publication date: 01/10/2016
Acceptance date: 28/07/2015
ISSN (print): 1846-3886
ISSN (electronic): 1848-9974
Publisher: Element d.o.o.
URL: http://dx.doi.org/10.7153/oam-10-48
DOI: 10.7153/oam-10-48
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