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Boundary representations for families of representations of operator algebras and spaces

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.

Publication metadata

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