Complete isometries between subspaces of noncommutative Lp-spaces
Operator Algebras
2017-11-07 v2 Functional Analysis
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.
Cite
@article{arxiv.0707.0427,
title = {Complete isometries between subspaces of noncommutative Lp-spaces},
author = {Mikael de la Salle},
journal= {arXiv preprint arXiv:0707.0427},
year = {2017}
}
Comments
30 pages; revised version of the paper with previous title "Equimeasurabily and isometries in noncommutative Lp-spaces". Changes in the title, presentation and content. Added results on unbounded operators, and applications