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Noncommutative Lp structure encodes exactly Jordan structure

David Sherman
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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.

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David Sherman. 2004-09-14. Noncommutative Lp structure encodes exactly Jordan structure. https://arxiv.org/abs/math/0309365

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