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arXiv · 1711.11090

Rational dilation problems associated with constrained algebras

Michael A. Dritschel·Batzorig Undrakh
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Abstract

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.

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Michael A. Dritschel, Batzorig Undrakh. 2017-11-29. Rational dilation problems associated with constrained algebras. https://arxiv.org/abs/1711.11090

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