Integral mappings and the principle of local reflexivity for noncommutative L^1spaces
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2000
 arXiv:
 arXiv:math/0008032
 Bibcode:
 2000math......8032E
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Functional Analysis;
 47D15;
 46B07;
 46B08
 EPrint:
 33 pages