The failure of rational dilation on a triply connected domain
Functional Analysis
2016-09-07 v1 Operator Algebras
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.
Cite
@article{arxiv.math/0310398,
title = {The failure of rational dilation on a triply connected domain},
author = {Michael A. Dritschel and Scott McCullough},
journal= {arXiv preprint arXiv:math/0310398},
year = {2016}
}
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43 pages