On the Banach-isomorphic classification of Lp spaces of hyperfinite von Neumann algebras

There are precisely thirteen Banach isomorphism types among the L-p-spaces associated with semifinite von Neumann algebras, for 1 less than or equal to p < <infinity>, p not equal 2. In particular, the preduals of the hyperfinite factors of types II1 and IIinfinity are isomorphically distinct Banach spaces. This situation differs markedly from the purely infinite setting: we show that the L-p-spaces associated with the hyperfinite factors IIIlambda are pairwise isomorphic for all 0 < <lambda> less than or equal to 1 and 1 less than or equal to p < <infinity>. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier. SAS.