Approximate innerness of positive linear maps of finite von Neumann algebras
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- by Hideo Takemoto PDF
- Proc. Amer. Math. Soc. 94 (1985), 463-466 Request permission
Abstract:
Let $M$ be a $\sigma$-finite, finite von Neumann algebra with a faithful, normalized, normal trace Tr and a positive linear map $\rho$ of $M$ into itself. If $\rho$ is approximately inner with respect to the norm $||.|{|_2}$ induced by Tr, then $\rho$ is closely related to a $*$-homomorphism. In particular, if $\rho$ is unital and approximately inner, then $\rho$ is a $*$-homomorphism of $M$ into itself.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 463-466
- MSC: Primary 46L10
- DOI: https://doi.org/10.1090/S0002-9939-1985-0787895-9
- MathSciNet review: 787895