Noncommutative Lp structure encodes exactly Jordan structure
Abstract
Description
We prove that for all 1 \le p \le \infty, p not 2, the Lp spaces associated to two von Neumann algebras M,N are isometrically isomorphic if and only 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.
14 pages, to appear in J. Funct. Anal. A step in the earlier proof was invalid for finite type I algebras
14 pages, to appear in J. Funct. Anal. A step in the earlier proof was invalid for finite type I algebras