Noncommutative Lp structure encodes exactly Jordan structure

We prove that for all 1 p ∞, p = 2, the Lp spaces associatedto two von Neumann algebras M, N are isometrically isomorphic if andonly if M and N are Jordan *-isomorphic. This follows from a noncommutative Lp Banach–Stone theorem: a specific decomposition for surjective isometries of noncommutative Lp spaces. © 2004 Elsevier Inc. All rights reserved