Noncommutative Lp structure encodes exactly Jordan structure

Details Noncommutative Lp structure encodes exactly Jordan structure Noncommutative Lp structure encodes exactly Jordan structure

2003-09-22

arxiv.org/abs/math/0309365v2

Mathematics

Operator Algebras

14 pages, to appear in J. Funct. Anal. A step in the earlier proof was invalid for finite type I algebras

Scientific paper

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.

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