Fubini Products of $C^{\ast }$-algebras and Applications to $C^{\ast }$-exactness

Abstract

For $C^{\ast }$-algebras $A$ and $B$, we investigate necessary and sufficient conditions for which the Fubini product $A{\otimes }_{F}B$ coincides with the ordinary minimal tensor product $A\otimes B$. As an application of our methods, we also give several necessary and sufficient conditions for $C^{\ast }$-exactness.