6 research outputs found
Rational dilation problems associated with constrained algebras
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.Comment: Page proof corrections included in this version