Embedding of OH and logarithmic `little Grothendieck inequality'

Details Embedding of OH and logarithmic `little Grothendieck inequality' Embedding of OH and logarithmic `little Grothendieck inequality'

2004-10-08

arxiv.org/abs/math/0410235v1

Mathematics

Operator Algebras

Scientific paper

10.1007/s00222-004-0421-0

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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