Let $ A$ be a non-nuclear $ C^*$ -algebra and $ I$ be a closed ideal of it. For what kind of Banach algebra $ A$ , $ A/I$ is nuclear?( I mean is there any example of non-nuclear $ C^*$ -algebra with a nuclear quotient?)Read more
Let $ A$ be a non-nuclear $ C^*$ -algebra and $ I$ be a closed ideal of it. For what kind of Banach algebra $ A$ , $ A/I$ is nuclear?( I mean is there any example of non-nuclear $ C^*$ -algebra with a nuclear quotient?)Read more
In very rough terms, let $ A$ be a complex unital $ C^*$ -algebra. Assume it nuclear for convenience, but it doesn’t matter much. Consider the ‘Fock’-type $ C^*$ -algebra (don’t know a better name for it) $ $ \mathbb{C}\bigoplus A\bigoplus A\otimes A\bigoplus\ldots $ $ This can be thought of as the $ C^*$ -algebraRead more
Let $ G$ be a finite abelian group (cosidered as a discrete topological group), $ A$ a unital separable $ C^*$ -algebra. Let $ T\colon G\to \operatorname{Aut}(A)$ , $ T_g(a)=a$ for all $ g\in G$ the trivial action. Let $ Lt\colon G\to \operatorname{Aut}(C(G))$ the left translation, i.e. $ Lt$ is given by $ Lt_g(f)(h)=f(g^{-1}h)$ forRead more