Geodesic
Failure of the trilinear operator space Grothendieck theorem
Discrete analysis (2019) Cet article a éte moissonné depuis la source Scholastica

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We give a counterexample to a trilinear version of the operator space Grothendieck theorem. In particular, we show that for trilinear forms on $\ell_\infty$, the ratio of the symmetrized completely bounded norm and the jointly completely bounded norm is in general unbounded, answering a question of Pisier. The proof is based on a non-commutative version of the generalized von Neumann inequality from additive combinatorics.
Publié le : 
@article{DAS_2019_a12,
     author = {Jop Bri\"et and Carlos Palazuelos},
     title = {Failure of the trilinear operator space {Grothendieck} theorem},
     journal = {Discrete analysis},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2019_a12/}
}
TY  - JOUR
AU  - Jop Briët
AU  - Carlos Palazuelos
TI  - Failure of the trilinear operator space Grothendieck theorem
JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a12/
LA  - en
ID  - DAS_2019_a12
ER  - 
%0 Journal Article
%A Jop Briët
%A Carlos Palazuelos
%T Failure of the trilinear operator space Grothendieck theorem
%J Discrete analysis
%D 2019
%U http://geodesic.mathdoc.fr/item/DAS_2019_a12/
%G en
%F DAS_2019_a12
Jop Briët; Carlos Palazuelos. Failure of the trilinear operator space Grothendieck theorem. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a12/