Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains

Details Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains

2007-11-26

arxiv.org/abs/0711.4080v2

Mathematics

Functional Analysis

Post-refereed version

Scientific paper

10.1007/s11785-008-0079-5

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.

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