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Integral mappings and the principle of local reflexivity for noncommutative L^1-spaces

Edward G. Effros·Marius Junge·Zhong-Jin Ruan
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Abstract

The operator space analogue of the {\em strong form} of the principle of local reflexivity is shown to hold for any von Neumann algebra predual, and thus for any $C^{*}$-algebraic dual. This is in striking contrast to the situation for $C^{*}$-algebras, since, for example, $K(H)$ does not have that property. The proof uses the Kaplansky density theorem together with a careful analysis of two notions of integrality for mappings of operator spaces.

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Edward G. Effros, Marius Junge, Zhong-Jin Ruan. 2000-08-03. Integral mappings and the principle of local reflexivity for noncommutative L^1-spaces. https://arxiv.org/abs/math/0008032

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