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Decomposition of an order isomorphism between matrix-ordered Hilbert spaces

Author: Yasuhide Miura
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1973-1977
MSC (2000): Primary 46L10, 46L40
Published electronically: February 6, 2004
MathSciNet review: 2053968
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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.

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Additional Information

Yasuhide Miura
Affiliation: Department of Mathematics, Faculty of Humanities and Social Sciences, Iwate University, Morioka, 020-8550, Japan

Keywords: Order isomorphism, completely positive map, matrix-ordered Hilbert space
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
Article copyright: © Copyright 2004 American Mathematical Society