Noncommutative Lp structure encodes exactly Jordan structure
Operator Algebras
2007-05-23 v2
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.
Cite
@article{arxiv.math/0309365,
title = {Noncommutative Lp structure encodes exactly Jordan structure},
author = {David Sherman},
journal= {arXiv preprint arXiv:math/0309365},
year = {2007}
}
Comments
14 pages, to appear in J. Funct. Anal. A step in the earlier proof was invalid for finite type I algebras