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Proceedings of the American Mathematical Society

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

 

 

Decomposable positive maps on $ C\sp{\ast} $-algebras


Author: Erling Størmer
Journal: Proc. Amer. Math. Soc. 86 (1982), 402-404
MSC: Primary 46L05
MathSciNet review: 671203
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Abstract: It is shown that a positive linear map of a $ {C^*}$-algebra $ A$ into $ B(H)$ is decomposable if and only if for all $ n \in {\mathbf{{\rm N}}}$ whenever $ ({x_{ij}})$ and $ ({x_{ji}})$ belong to $ {M_n}{(A)^ + }$ then $ (\phi ({x_{ij}}))$ belongs to $ {M_n}{(B(H))^ + }$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0671203-5
Keywords: Positive maps
Article copyright: © Copyright 1982 American Mathematical Society