Embedding of the operator space OH and the logarithmic 'little Grothendieck inequality'

• 成果类型: Article
• 署名作者: Junge, M
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0421-0
• 发表日期: 2005
• 页码: 225-286
• 关键词: von-neumann algebra; free-products; THEOREM; exactness; MAPS

摘要

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 OHn: 108(1) root 1 + ln(n) n (<=) P: B(l(2)) --> OHninf, P-2 = P parallel to P parallel to(cb) <= 288 pi root 1 + ln(2n) 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/root 1 + ln n indicates that the operator space OHn behaves differently than its classical counterpart l(2)(n). We give an application of this formula to positive sesquilinear forms on B(l(2)). This leads to logarithmic characterization of C*-algebras with the weak expectation property introduced by Lance.