Failure of the trilinear operator space Grothendieck theorem

Briët, Jop; Palazuelos, Carlos

doi:10.19086/da.8805

We give a counterexample to a trilinear version of the operator space Grothendieck theorem. In particular, we show that for trilinear forms on ℓ∞, the ratio of the symmetrized completely bounded norm and the jointly completely bounded norm is in general unbounded. The proof is based on a non-commutative version of the generalized von Neumann inequality from additive combinatorics.

Additional Metadata
Keywords	Grothendieck theorem, Operator spaces, Additive combinatorics
Persistent URL	doi.org/10.19086/da.8805
Journal	Discrete Analysis
Project	Quantum and classical data transmission
Grant	This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/639.071.409 - Quantum and classical data transmission
Organisation	Algorithms and Complexity
Citation APA Style AAA Style APA Style Cell Style Chicago Style Harvard Style IEEE Style MLA Style Nature Style Vancouver Style American-Institute-of-Physics Style Council-of-Science-Editors Style BibTex Format Endnote Format RIS Format CSL Format DOIs only Format	Briët, J, & Palazuelos, C. (2019). Failure of the trilinear operator space Grothendieck theorem. Discrete Analysis, (8). doi:10.19086/da.8805

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