2017/11/29 by Dritschel, Michael A., Undrakh, Batzorig
#30C40 #30E05 #46E22 #46E25 #46E40 #46L07 #47A20 (Primary) #47A25 #47A48 #47L55 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1711.11090
It is shown that rational dilation fails on broad collection of distinguished varieties associated to constrained subalgebras of the disk algebra of the form C + B A(D), where B is a finite Blaschke product with two or more zeros. This is accomplished in part by finding a minimal set of test functions. In addition, an Agler-Pick interpolation theorem is given and it is proved that there exist Kaijser-Varopoulos style examples of non-contractive unital representations where the generators are contractions.