2019-06-04
Failure of the trilinear operator space Grothendieck theorem
Publication
Publication
Discrete Analysis
Issue 8
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 | |
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| Keywords | Grothendieck theorem, Operator spaces, Additive combinatorics |
| Persistent URL | dx.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 |
| Citation |
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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