Effective Dimensions in Grothendieck--Hölder Inequalities

Joedson Santos, Diana Serrano-Rodríguez

What becomes of Grothendieck's inequality when its Hilbert-space vectors are replaced by vectors in ${\ell }_p^r$ and ${\ell }_{p^{\prime }}^r$? For an $m\times n$ matrix, we show that the univer…