English

Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains

Functional Analysis 2008-09-02 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0711.4080,
  title  = {Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains},
  author = {James Pickering},
  journal= {arXiv preprint arXiv:0711.4080},
  year   = {2008}
}

Comments

Post-refereed version

R2 v1 2026-06-21T09:47:23.275Z