Decomposition of an order isomorphism between matrix-ordered Hilbert spaces
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- by Yasuhide Miura PDF
- Proc. Amer. Math. Soc. 132 (2004), 1973-1977 Request permission
Abstract:
The purpose of this note is to show that any order isomorphism between noncommutative $L^{2}$-spaces associated with von Neumann algebras is decomposed into a sum of a completely positive map and a completely co-positive map. The result is an $L^{2}$ version of a theorem of Kadison for a Jordan isomorphism on operator algebras.References
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Additional Information
- Yasuhide Miura
- Affiliation: Department of Mathematics, Faculty of Humanities and Social Sciences, Iwate University, Morioka, 020-8550, Japan
- Email: ymiura@iwate-u.ac.jp
- Received by editor(s): March 6, 2003
- Published electronically: February 6, 2004
- Additional Notes: This research was partially supported by the Grants-in-Aid for Scientific Research, The Ministry of Education, Culture, Sports, Science and Technology, Japan
- Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1973-1977
- MSC (2000): Primary 46L10, 46L40
- DOI: https://doi.org/10.1090/S0002-9939-04-07454-4
- MathSciNet review: 2053968