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Lookup NU author(s): Dr Michael DritschelORCiD
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In analogy with the peak points of the Shilov boundary of a uniform algebra, Arveson defined the notion of boundary representations among the completely contractive representations of a unital operator algebra. However, he was unable to show that such representations always exist. Dropping his original condition that such representations should be irreducible, we show that a family of representations (in Agler's sense) of either an operator algebra or an operator space has boundary representations. This leads to a direct proof of Hamana's result that all unital operator algebras have enough such boundary representations to generate the C*-envelope. © Copyright by THETA, 2005.
Author(s): Dritschel MA, Mccullough SA
Publication type: Article
Publication status: Published
Journal: Journal of Operator Theory
Year: 2005
Volume: 53
Issue: 1
Pages: 159-167
Print publication date: 01/12/2005
ISSN (print): 0379-4024
ISSN (electronic):
Publisher: Academia Romana, Institutul de Matematica
URL: http://www.mathjournals.org/jot/2005-053-001/2005-053-001-006.pdf