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Dilations and Constrained Algebras

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.

Publication metadata

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.


DOI: 10.7153/oam-10-48


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Funder referenceFunder name
DMS 1101461NSF
DMS 1101137NSF