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Proceedings of the American Mathematical Society

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Approximate innerness of positive linear maps of finite von Neumann algebras. II


Authors: Chôichirô Sunouchi and Hideo Takemoto
Journal: Proc. Amer. Math. Soc. 101 (1987), 662-666
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1987-0911029-2
MathSciNet review: 911029
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Abstract: Let $ M$ be a $ \sigma $-finite, finite von Neumann algebra with a faithful, normalized normal trace Tr on $ M$. Let $ \rho $ be a positive linear map of $ M$ into itself such that $ \rho (1)$ is not necessarily a projection. If $ \rho $ is approximately inner with respect to the norm $ \vert\vert.\vert{\vert _2}$ induced by Tr, then $ \rho $ has a close connection to $ {*}$-homomorphisms.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0911029-2
Article copyright: © Copyright 1987 American Mathematical Society