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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The unique representation of a selfadjoint bounded linear functional


Author: Ching Yun Suen
Journal: Proc. Amer. Math. Soc. 95 (1985), 58-62
MSC: Primary 46L30; Secondary 46L05
MathSciNet review: 796446
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Abstract: It is well known that every selfadjoint bounded linear functional on a $ {C^ * }$-algebra has a unique minimal decomposition [6, Theorem 3.2.5]. In this paper we prove that under some conditions a selfadjoint completely bounded linear map with a unique minimal decomposition is equivalent to the map with a unique commutant representation (up to unitary equivalence). Using the results, we generalize the Gel'fand-Naimark-Segal construction.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0796446-4
PII: S 0002-9939(1985)0796446-4
Article copyright: © Copyright 1985 American Mathematical Society