Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains
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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.
Mathematics Subject Classification (2000).Primary 47A20 Secondary 47A25, 47A48, 46E22, 30C20, 30H05, 30F10, 30E05
Keywords.Rational dilation hyperelliptic Riemann surfaces Nevanlinna–Pick interpolation
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