One more pathology of C*-algebraic tensor products

TL;DR

This paper introduces new tensor product norms for C*-algebras and demonstrates that symmetric tensor product functors may lack associativity, revealing limitations in existing tensor product frameworks.

Contribution

It defines novel tensor product norms and shows that symmetric tensor product functors are not necessarily associative in the category of separable C*-algebras.

Findings

New tensor product norms for C*-algebras are proposed.

Symmetric tensor product functors can be non-associative.

Highlights limitations in current tensor product theories.

Abstract

We define a collection of tensor product norms for C*-algebras and show that a symmetric tensor product functor on the category of separable C*-algebras need not be associative.