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The failure of rational dilation on a triply connected domain

Michael A. Dritschel·Scott McCullough
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Abstract

For R a bounded triply connected domain with boundary consisting of disjoint Jordan loops there exists an operator T on a complex Hilbert space 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 Rafael using numerical computations and work of Agler and Harland.

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Michael A. Dritschel, Scott McCullough. 2003-10-24. The failure of rational dilation on a triply connected domain. https://arxiv.org/abs/math/0310398

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