Nuclear C*-algebra

Summary

A nuclear C*-algebra is a C*-algebra whose algebraic tensor product with any other C*-algebra has only one C*-norm. Equivalently, the identity map of the algebra can be approximated by completely positive maps that factor through matrix algebras. Nuclearity is a finiteness or amenability property: for C*-algebras it is equivalent to amenability as a Banach algebra. It is a standing hypothesis in the classification program for simple C*-algebras.