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

Sunouchi, Chôichirô; Takemoto, Hideo

doi:10.1090/S0002-9939-1987-0911029-2

Approximate innerness of positive linear maps of finite von Neumann algebras. II
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by Chôichirô Sunouchi and Hideo Takemoto PDF

Proc. Amer. Math. Soc. 101 (1987), 662-666 Request permission

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 $||.|{|_2}$ induced by Tr, then $\rho$ has a close connection to ${*}$-homomorphisms.

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Complete positivity in operator algebras