Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains

被引：6

作者：

Pickering, James ^{[1
]}

机构：

[1] Newcastle Univ, Dept Math, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2010年 / 4卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Rational dilation; hyperelliptic Riemann surfaces; Nevanlinna-Pick interpolation;

D O I：

10.1007/s11785-008-0079-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that if R is a compact domain in the complex plane with two or more holes and an anticonformal involution onto itself (or equivalently a hyperelliptic Schottky double), then there is an operator T which has R as a spectral set, but does not dilate to a normal operator with spectrum on the boundary of R.

引用

页码：55 / 95

页数：41

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