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arXiv · 1812.09726

Failure of the trilinear operator space Grothendieck theorem

Jop Briët·Carlos Palazuelos
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Abstract

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.

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Jop Briët, Carlos Palazuelos. 2019-06-03. Failure of the trilinear operator space Grothendieck theorem. https://doi.org/10.19086/da.8805

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