The failure of rational dilation on a triply connected domain

Dritschel, Michael; McCullough, Scott

doi:10.1090/S0894-0347-05-00491-1

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.

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