Approximate innerness of positive linear maps of finite von Neumann algebras

Author:
Hideo Takemoto

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

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Abstract: Let be a -finite, finite von Neumann algebra with a faithful, normalized, normal trace Tr and a positive linear map of into itself. If is approximately inner with respect to the norm induced by Tr, then is closely related to a -homomorphism. In particular, if is unital and approximately inner, then is a -homomorphism of into itself.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0787895-9

Keywords:
Approximate innerness,
trace,
completely positive map,
finite von Neumann algebra

Article copyright:
© Copyright 1985
American Mathematical Society