The failure of rational dilation on a triply connected domain

Dritschel, Michael¹ ; McCullough, Scott²

¹ School of Mathematics and Statistics, Merz Court, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom
² Department of Mathematics, University of Florida, Box 118105, Gainesville, Florida 32611-8105

Journal of the American Mathematical Society, Tome 18 (2005) no. 4, pp. 873-918

Résumé

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.

Détail

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

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