Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains
arXiv:0711.4080 · doi:10.1007/s11785-008-0079-5
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.
Post-refereed version