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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The failure of rational dilation on a triply connected domain
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by Michael A. Dritschel and Scott McCullough PDF
J. Amer. Math. Soc. 18 (2005), 873-918 Request permission


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.
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Additional 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:
  • Scott McCullough
  • Affiliation: Department of Mathematics, University of Florida, Box 118105, Gainesville, Florida 32611-8105
  • MR Author ID: 220198
  • Email:
  • 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:
  • MathSciNet review: 2163865