Elementary proofs of grothendieck theorems for completely bounded norms

Oded Regev, Thomas Vidick

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)491-506
Number of pages16
JournalJournal of Operator Theory
Volume71
Issue number2
DOIs
StatePublished - 2014

Fingerprint

Bilinear form
Norm
Theorem
Quantum Information Theory
Operator Space
C*-algebra
Alternatives
Estimate

Keywords

  • Bilinear form
  • Completely bounded norm
  • Grothendieck inequality
  • Quantum information theory

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Elementary proofs of grothendieck theorems for completely bounded norms. / Regev, Oded; Vidick, Thomas.

In: Journal of Operator Theory, Vol. 71, No. 2, 2014, p. 491-506.

Research output: Contribution to journalArticle

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