Complete isometries between subspaces of noncommutative Lp-spaces

Mikael de la Salle

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arXiv · 0707.0427

Complete isometries between subspaces of noncommutative Lp-spaces

Mikael de la Salle

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Abstract

We prove some noncommutative analogues of a theorem by Plotkin and Rudin about isometries between subspaces of Lp-spaces. Let 0<p<\infty, p not an even integer. The main result of this paper states that in the category of unital subspaces of noncommutative probability Lp-spaces, under some boundedness condition, the unital completely isometric maps come from *-isomorphisms of the underlying von Neumann algebras. Some applications are given, including to non commutative H^p spaces.

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Mikael de la Salle. 2007-12-04. Complete isometries between subspaces of noncommutative Lp-spaces. https://arxiv.org/abs/0707.0427

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