Completely bounded maps into certain Hilbertian operator spaces

2004/03/13 by Gilles Pisier, Pisier, Gilles
Mathematics · #46L07 #46L54 #47L25 #47L50 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.FA #math.OA #msc:46L07 #msc:46L54 #msc:47L25 #msc:47L50

paper · pdf · doi:10.48550/arxiv.math/0403220

Minor corrections of misprints and addition of an introduction

openalex publication_date 2004/03/13 · arxiv created 2004/07/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a factorization of completely bounded maps from a C^*-algebra A (or an exact operator space E⊂ A) to ℓ₂ equipped with the operator space structure of (C,R)_θ (00 such that ∀ a∈ A ‖ua‖²≤ C f(a^*a)^1-θg(aa^*)^θ. This extends the case θ=1/2 treated in a recent paper with Shlyakhtenko. The constants we obtain tend to 1 when θ→ 0 or θ→ 1. We use analogues of "free Gaussian" families in non semifinite von Neumann algebras. As an application, we obtain that, if 0

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