Failure of the trilinear operator space Grothendieck theorem
Failure of the trilinear operator space Grothendieck theorem
Failure of the trilinear operator space Grothendieck theorem, Discrete Analysis 2019:8, 16 pp. Let $\beta:\ell_\infty^n\times \ell_\infty^n\to\mathbb C$ be a bilinear form. We define its operator norm by the formula $$\|\beta\|=\sup\{|\beta(x,y)|:\|x\|_\infty=\|y\|_\infty=1\}.$$ Let $(A_{ij})$ be the matrix of $\beta$, so that $$\beta(x,y)=\sum_{ij}A_{ij}x_iy_j.$$ This second formula can be generalized in interesting ways. For …