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Decomposition of an order isomorphism between matrix-ordered Hilbert spaces

Authors:	Yasuhide Miura

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

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.

Keywords:	Order isomorphism completely positive map matrix-ordered Hilbert space

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