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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. doi:10.7900/jot.2012jul02.1947.

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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
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URLURL TypeDescription Paper
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.
Funding AgencyGrant Number
European Research Council (ERC)UNSPECIFIED
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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65489
Deposited By: Tony Diaz
Deposited On:18 Mar 2016 22:29
Last Modified:10 Nov 2021 23:46

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