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- W2953053782 abstract "Using free random varaibles we find an embedding of the operator space $OH$ in the predual of a von Neumann algebra. The properties of this embedding allow us to determined the projection constant of $OH_n$, i.e. there exists a projection $P:B(ell_2)to OH_n$ whose completely bounded norm behaves as n^{1/2}/(1+ln n)^{1/2}. According to recent results of Pisier/Shlyahtenko, the lower bound holds for every projection. Improving a previous estimate of order $(1+ ln n)$ of the author, Pisier/Shlyahtenko obtained a `logarithmic little Grothendieck inequality'. We find a second proof of this inequality which explains why the factor $sqrt{1+ln n}$ is indeed necessary. In particular the operator space version of the `little Grothendieck inequality' fails to hold. This `logarithmic little Grothendieck' inequality characterizes $C^*$-algebras with the weak expectation property of Lance." @default.
- W2953053782 created "2019-06-27" @default.
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- W2953053782 date "2003-05-27" @default.
- W2953053782 modified "2023-09-27" @default.
- W2953053782 title "Embedding of the operator space OH and the logarithmic `little Grothendieck inequality'" @default.
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