CaltechAUTHORS
  A Caltech Library Service

Elementary Proofs of Grothendieck Theorems for Completely Bounded Norms

Regev, Oded and Vidick, Thomas (2014) Elementary Proofs of Grothendieck Theorems for Completely Bounded Norms. Journal of Operator Theory, 71 (2). pp. 491-506. ISSN 1841-7744. https://resolver.caltech.edu/CaltechAUTHORS:20160318-152323237

[img] PDF - Submitted Version
See Usage Policy.

241Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20160318-152323237

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, Invent. Math. 150(2002), 185-217) and Haagerup and Musat (The Effros-Ruan conjecture for bilinear forms on C*-algebras, Invent. Math. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.7900/jot.2012jul02.1947DOIArticle
https://arxiv.org/abs/1206.4025arXivDiscussion Paper
ORCID:
AuthorORCID
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2014 by THETA. Received July 2, 2012; posted on June 1, 2014. We thank Gilles Pisier for allowing us to include Claim A.3. We also thank him and Carlos Palazuelos for useful comments. O. Regev's research was supported by an European Research Council (ERC) Starting Grant. T. Vidick's research was supported by the U.S. National Science Foundation under Grant No. 0844626.
Funders:
Funding AgencyGrant Number
European Research Council (ERC)UNSPECIFIED
NSFCCF-0844626
Subject Keywords:Grothendieck inequality, quantum information theory, bilinear form, completely bounded norm
Issue or Number:2
Classification Code:MSC (2010): 46L07, 47L25
Record Number:CaltechAUTHORS:20160318-152323237
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160318-152323237
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65489
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Mar 2016 22:29
Last Modified:29 Jul 2020 22:32

Repository Staff Only: item control page