The Operator Hilbert Space OH and TYPE III von Neumann Algebras
Operator Algebras
2007-05-23 v2 Functional Analysis
Abstract
We prove that the operator Hilbert space OH does not embed completely isomorphically into the predual of a semi-finite von Neumann algebra. This complements Junge's recent result that it admits such an embedding in the non semi-finite case.
Keywords
Cite
@article{arxiv.math/0209019,
title = {The Operator Hilbert Space OH and TYPE III von Neumann Algebras},
author = {Gilles Pisier},
journal= {arXiv preprint arXiv:math/0209019},
year = {2007}
}
Comments
Minor improvements, a simplification, and the observation that the same result is valid with OH replaced by $(R,C)_\theta$ ($0< \theta<1$)