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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A proof of the boundary theorem


Author: Kenneth R. Davidson
Journal: Proc. Amer. Math. Soc. 82 (1981), 48-50
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1981-0603599-3
MathSciNet review: 603599
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Abstract: This note contains a simple proof of the following theorem of Arveson: If $ \mathcal{A}$ is an irreducible subspace of $ \mathcal{B}(H)$, then the identity map $ {\phi _0}(A) = A$ on $ \mathcal{A}$ has a unique completely positive extension to $ \mathcal{B}(H)$ if and only if the quotient map $ q$ by the compact operators is not completely isometric on $ \mathcal{S} = [\mathcal{A} + \mathcal{A}^*]$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0603599-3
Keywords: Completely positive maps, lifting problem, Calkin algebra
Article copyright: © Copyright 1981 American Mathematical Society