Complex Analysis and Operator Theory

, Volume 4, Issue 1, pp 55–95 | Cite as

Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains

Article

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.

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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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Newcastle-upon-TyneNewcastle-upon-TyneUnited Kingdom

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