Is there a non nuclear $C^\*$ algebra $A$ for which the minimum and maximum $C^\*$ norms on $A\otimes A$ coincide?


A somewhat similar question is [discussed here](https://mathoverflow.net/questions/127971/).



A non nuclear $C^*$ algebra $A$ for which the algebraic tensor product $A\otimes A$ admits a unique $C^*$ norm
Pisier <https://arxiv.org/abs/1908.02705> very recently constructed a non-nuclear $C^\ast$-algebra $A$ with the weak expectation property (WEP) and the local lifting property (LLP). By a celebrated result of Kirchberg (see Corollary 13.2.5 in Brown and Ozawa's book) it follows that if $B$ has WEP and $C$ has LLP, then $B\otimes\_{\max{}} C = B\otimes\_{\min{}} C$. Hence $A\otimes\_{\max{}} A = A\otimes\_{\min{}} A$.


