Nuclear C^*-Algebra

A nuclear -algebra is a C^*-algebra for which the minimal and maximal C^*-algebra tensor products with every C^*-algebra coincide. Equivalently, the algebraic vector space tensor product has a unique -norm. This is a property of the algebra, not of a particular Hilbert space representation. Matrix algebras and commutative C^*-algebras are examples. Kirchberg's embedding problem concerns embeddings into norm ultrapowers of the nuclear Cuntz algebra .