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Lookup NU author(s): Dr Michael DritschelORCiD
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Agler's abstract model theory is applied to $\Crho$, the family of operators with unitary $\rho$-dilations, where $\rho$ is a fixed number in $(0,2]$. The extremals, which are the collection of operators in $\Crho$ with the property that the only extensions of them which remain in the family are direct sums, are characterized in a variety of manners. They form a part of any model, and in particular, of the boundary, which is defined as the smallest model for the family. Any model for a family is required to be closed under direct sums, restrictions to reducing subspaces, and unital $*$-representations. In the case of the family $\Crho$ with $\rho\in(0,1)\cup(1,2]$, this closure is shown to be all of $\Crho$.
Author(s): Dritschel MA, McCullough S, Woerdeman HJ
Publication type: Article
Publication status: Published
Journal: Journal of Operator Theory
Print publication date: 01/01/1999
ISSN (print): 0379-4024
Publisher: The Theta Foundation