2013/05/18 by Michael A. Dritschel, Dritschel, Michael A., Michael T. Jury +3 · 2 citations
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1305.4272
New to version 2 is a proof of rational dilation for the distinguished variety in the bidisk determined by (z-w)(z+w)=0
arxiv created 2013/10/17 · arxiv updated 2013/10/18
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.