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: 1/108√n/1+ln n ≤ inf P:B(ℓ2)→OHn, P2=P ∥P∥cb≤ 288π√2n/1+ln n. 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 indicates that the operator space OH n behaves differently than its classical counterpart ℓ2n. We give an application of this formula to positive sesquilinear forms on B(ℓ2). This leads to logarithmic characterization of C*-algebras with the weak expectation property introduced by Lance.
Original language | English (US) |
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Pages (from-to) | 225-286 |
Number of pages | 62 |
Journal | Inventiones Mathematicae |
Volume | 161 |
Issue number | 2 |
DOIs | |
State | Published - Aug 2005 |
ASJC Scopus subject areas
- General Mathematics