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Decomposition of an order isomorphism between matrix-ordered Hilbert spaces
Author(s):
Yasuhide
Miura
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1973-1977.
MSC (2000):
Primary 46L10, 46L40
Posted:
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  -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  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
DOI:
10.1090/S0002-9939-04-07454-4
PII:
S 0002-9939(04)07454-4
Keywords:
Order isomorphism,
completely positive map,
matrix-ordered Hilbert space
Received by editor(s):
March 6, 2003
Posted:
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 of article:
Copyright
2004,
American Mathematical Society
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