Abstract
We show that boundary representations of an operator algebra may be characterized as those (irreducible) completely contractive representations that determine Hilbert modules that are simultaneously orthogonally projective and orthogonally injective. As a corollary, we conclude that if an operator algebra is an admissable subalgebra of its C * —envelope, in the sense of Arveson, then it has a completely isometric representation such that the associated Hilbert module is simultaneously orthogonally projective and orthogonally injective.
Supported in part by grants from the National Science Foundation and the U.S.-Israel Binational Science Foundation.
Supported in part by the U.S.-Israel Binational Science Foundation and by the Fund for the Promotion of Research at the Technion.
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© 1998 Springer Basel AG
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Muhly, P.S., Solel, B. (1998). An Algebraic Characterization of Boundary Representations. In: Bercovici, H., Foias, C.I. (eds) Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics. Operator Theory Advances and Applications, vol 104. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8779-3_13
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DOI: https://doi.org/10.1007/978-3-0348-8779-3_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9771-6
Online ISBN: 978-3-0348-8779-3
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