# Elementary proofs of Grothendieck theorems for completely bounded norms

1 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Grothendieck's theorem for operator spaces, \textit{Invent. Math.} \textbf{150}(2002), 185--217) and Haagerup and Musat (The Effros-Ruan conjecture for bilinear forms on ${C}^*$-algebras, \textit{Invent. Math.} \textbf{174}(2008), 139--163). Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.
Keywords :
Type de document :
Article dans une revue
Journal of Operator Theory, 2012, 71 (2), pp.491-506. 〈10.7900/jot.2012jul02.1947 〉

https://hal.inria.fr/hal-01111570
Contributeur : Brigitte Briot <>
Soumis le : vendredi 30 janvier 2015 - 15:43:51
Dernière modification le : vendredi 25 mai 2018 - 12:02:05

### Citation

Oded Regev, Thomas Vidick. Elementary proofs of Grothendieck theorems for completely bounded norms . Journal of Operator Theory, 2012, 71 (2), pp.491-506. 〈10.7900/jot.2012jul02.1947 〉. 〈hal-01111570〉

### Métriques

Consultations de la notice