## The failure of rational dilation on a triply connected domain

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- by Michael A. Dritschel and Scott McCullough
- J. Amer. Math. Soc.
**18**(2005), 873-918 - DOI: https://doi.org/10.1090/S0894-0347-05-00491-1
- Published electronically: June 2, 2005
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## Abstract:

For $R$ a bounded triply connected domain with boundary consisting of disjoint analytic curves there exists an operator $T$ on a complex Hilbert space $\mathcal H$ so that the closure of $R$ is a spectral set for $T$, but $T$ does not dilate to a normal operator with spectrum in $B$, the boundary of $R$. There is considerable overlap with the construction of an example on such a domain recently obtained by Agler, Harland and Raphael using numerical computations and work of Agler and Harland.## References

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*A monograph on function theory and Herglotz formulas for multiply connected domains*. AHR Jim Agler, John Harland, and Benjamin Raphael,

*Classical function theory, operator dilation theory, and machine computations on multiply-connected domains*.

*Private communication*.

## Bibliographic Information

**Michael A. Dritschel**- Affiliation: School of Mathematics and Statistics, Merz Court, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom
- Email: m.a.dritschel@ncl.ac.uk
**Scott McCullough**- Affiliation: Department of Mathematics, University of Florida, Box 118105, Gainesville, Florida 32611-8105
- MR Author ID: 220198
- Email: sam@math.ufl.edu
- Received by editor(s): April 28, 2004
- Published electronically: June 2, 2005
- Additional Notes: The first author’s research was supported by the EPSRC

The second author’s research was supported by the NSF - © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**18**(2005), 873-918 - MSC (2000): Primary 47A25; Secondary 30C40, 30E05, 30F10, 46E22, 47A20, 47A48
- DOI: https://doi.org/10.1090/S0894-0347-05-00491-1
- MathSciNet review: 2163865