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Proceedings of the American Mathematical Society

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

 
 

 

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


Authors: Man Duen Choi and Sze Kai Tsui
Journal: Proc. Amer. Math. Soc. 87 (1983), 57-61
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1983-0677231-9
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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Keywords: <IMG WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^ * }$">-algebras, finite von Neumann algebras, positive linear maps, traces, Schwarz inequality, Toeplitz operators
Article copyright: © Copyright 1983 American Mathematical Society