2003/05/27 by Marius Junge, Junge, Marius · 1 citation
Mathematics · #46L53 #46L54 #47L25 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L53 #msc:46L54 #msc:47L25
paper · pdf · doi:10.48550/arxiv.math/0305387
arxiv created 2003/05/27 · openalex publication_date 2003/05/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 OHn, i.e. there exists a projection P:B(ℓ2)→ OHn whose completely bounded norm behaves as n1/2/(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 √(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.