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. https://resolver.caltech.edu/CaltechAUTHORS:20160318-152323237
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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.
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| 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. | |||||||||
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| Subject Keywords: | Grothendieck inequality, quantum information theory, bilinear form, completely bounded norm | |||||||||
| Issue or Number: | 2 | |||||||||
| Classification Code: | MSC (2010): 46L07, 47L25 | |||||||||
| DOI: | 10.7900/jot.2012jul02.1947 | |||||||||
| 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: | 10 Nov 2021 23:46 |
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