Noncommutative Lp structure encodes exactly Jordan structure

Abstract

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

References in corpus (2)

• On the structure of isometries between noncommutative Lp spaces
• A new proof of the noncommutative Banach-Stone theorem

Cited by in corpus (7)

• Tingley's problem through the facial structure of operator algebras
• Noncommutative Lp modules
• Transition probabilities of normal states determine the Jordan structure of a quantum system
• Symmetries of projective spaces and spheres
• W*-algebras and noncommutative integration
• On the structure of isometries between noncommutative Lp spaces
• Noncommutative Orlicz spaces over W*-algebras