Integral mappings and the principle of local reflexivity for noncommutative L¹-spaces

2000/08/03 by Edward G. Effros, Marius Junge, Zhong-Jin Ruan
Mathematics · #math.OA #math.FA #msc:47D15 #msc:46B07 #msc:46B08

paper · pdf

published as Ann. of Math. (2) 151 (2000), no. 1, 59--92 · 33 pages

arxiv created 2000/08/03 · arxiv updated 2009/11/30

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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