Abstract : Motivated by considerations from quantum information theory, we study the asymptotic behaviour of large tensor powers of normed spaces and of operators between them. We define the tensor radius of a finite-dimensional normed space $\mathrm{X}$ as the limit of the sequence $A_{k}^{1 / k}$, where $A_{k}$ is the equivalence constant between the projective and injective norms on $X^{\otimes} k$. We show in particular that Euclidean spaces are characterized by the property that their tensor radius equals their dimension.
Joint work with Alexander Müller-Hermes, arXiv:2110.12828

Keywords : tensor norms; projective norm; injective norm