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Proceedings of the American Mathematical Society

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Tracial positive linear maps of $ C\sp{\ast} $-algebras


Authors: Man Duen Choi and Sze Kai Tsui
Journal: Proc. Amer. Math. Soc. 87 (1983), 57-61
MSC: Primary 46L05
MathSciNet review: 677231
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Abstract: A positive linear map $ \Phi :\mathfrak{A} \to \mathfrak{B}$ between two $ {C^ * }$-algebras is said to be tracial if $ \Phi ({A_1}{A_2}) = \Phi ({A_2}{A_1})$ for all $ {A_i} \in \mathfrak{A}$. A tracial positive linear map $ \mathfrak{A} \to \mathcal{B}\left(\mathcal{H} \right)$ is analyzed as the composition of a tracial positive linear map $ \mathfrak{A} \to C(X)$ followed by a positive linear map $ C(X) \to \mathcal{B}\left( \mathcal{H} \right)$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0677231-9
Keywords: $ {C^ * }$-algebras, finite von Neumann algebras, positive linear maps, traces, Schwarz inequality, Toeplitz operators
Article copyright: © Copyright 1983 American Mathematical Society