Decomposition of an order isomorphism between matrix-ordered Hilbert spaces

Miura, Yasuhide

doi:10.1090/S0002-9939-04-07454-4

Decomposition of an order isomorphism between matrix-ordered Hilbert spaces
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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.

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