| Résume | Both the minimal and maximal tensor product norms on a pair of C*-algebras are defined in an "extrinsic" way in terms of representations of the C*-algebras involved. One might wonder if there could be an intrinsic definition of these norm. For example, one might wonder if either the minimal or maximal tensor norm on a sum of simple tensors could be calculated by some sort of formula using norms of *-polynomials of the elements appearing in the simple tensors. In this talk, I explain how to use model theory to formulate a precise version of this latter question. We then discuss two variants of the question: the global version (where such a formula should hold for all C*-algebras, perhaps relative to some elementary class) and, time permitting, the local version (where such a formula should hold only for the pair of C*-algebras involved). I will explain that the answer to the global questions for both the maximal and minimal tensor product norms is negative in general, while in the local case, we give some examples where the answer is negative. The latter examples use the quantum complexity results MIP*=RE and MIP^co=coRE. The work presented in this talk is joint with Thomas Sinclair.
No prior knowledge of C*-algebra theory will be assumed.
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