Published June 1, 2014
| Submitted
Journal Article
Open
Elementary Proofs of Grothendieck Theorems for Completely Bounded Norms
- Creators
- Regev, Oded
-
Vidick, Thomas
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.
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.Attached Files
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Additional details
- Eprint ID
- 65489
- DOI
- 10.7900/jot.2012jul02.1947
- Resolver ID
- CaltechAUTHORS:20160318-152323237
- European Research Council (ERC)
- CCF-0844626
- NSF
- Created
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2016-03-18Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field