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Proceedings of the American Mathematical Society

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Complete orthogonal decomposition homomorphisms between matrix ordered Hilbert spaces

Authors: Yasuhide Miura and Kiminao Nishiyama
Journal: Proc. Amer. Math. Soc. 129 (2001), 1137-1141
MSC (2000): Primary 46L10, 46L40
Published electronically: October 19, 2000
MathSciNet review: 1814150
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Abstract: The purpose of this paper is to show that a complete order homomorphism and a complete orthogonal decomposition homomorphism between the non-commutative $L^{2}$-spaces induce respectively an isomorphism and a $*$-isomorphism between the associated reduced von Neumann 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

Kiminao Nishiyama
Affiliation: Niitsu Senior High School, Niitsu, 956-0832, Japan

Keywords: Standard form of von Neumann algebra, completely positive map, matrix ordered Hilbert space, orthogonal decomposition homomorphism
Received by editor(s): July 7, 1999
Published electronically: October 19, 2000
Additional Notes: The first author’s research was partially supported by the Grants-in-Aid for Scientific Research, Ministry of Education, Japan
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society