Failure of the trilinear operator space Grothendieck theorem
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.
|Keywords||Grothendieck theorem, Operator spaces, Additive combinatorics|
|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|
Briët, J, & Palazuelos, C. (2019). Failure of the trilinear operator space Grothendieck theorem. Discrete Analysis, (8). doi:10.19086/da.8805