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

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

2000-08-03

arxiv.org/abs/math/0008032v1

Ann. of Math. (2) 151 (2000), no. 1, 59--92

Mathematics

Operator Algebras

33 pages

Scientific paper

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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