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 -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:
https://doi.org/10.1090/S0002-9939-1985-0796446-4

Article copyright:
© Copyright 1985
American Mathematical Society