Embedding of OH and logarithmic `little Grothendieck inequality'
Abstract
We use Voiculescu's concept of free probability to construct a completely isomorphic embedding of the operator space OH in the predual of a von Neumann algebra. We analyze the properties of this embedding and determine the operator space projection constant of OH_n: It is of the order (n/1+ln n)^{1/2} The lower estimate is a recent result of Pisier and Shlyakhtenko that improves an estimate of order 1/(1+ln n) of the author. The additional factor 1/(1+ln n)^{1/2} indicates that the operator space OH_n behaves differently than its classical counterpart l_2^n. We give an application of this formula to positive sesquilinear forms on B(H). This leads to logarithmic characterization of C*-algebras with the weak expectation property introduced by Lance.
Keywords
Cite
@article{arxiv.math/0410235,
title = {Embedding of OH and logarithmic `little Grothendieck inequality'},
author = {Marius Junge},
journal= {arXiv preprint arXiv:math/0410235},
year = {2009}
}