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arXiv · math/0410235

Embedding of OH and logarithmic `little Grothendieck inequality'

Marius Junge
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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.

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Marius Junge. 2004-10-08. Embedding of OH and logarithmic `little Grothendieck inequality'. https://doi.org/10.1007/s00222-004-0421-0

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