On closed Lie ideals of certain tensor products of $C^{\ast }$-algebras

Ranjana Jain, Ved Prakash Gupta

For a simple $C^{\ast }$-algebra $A$ and any other $C^{\ast }$-algebra $B$, it is proved that every closed ideal of $A{\otimes }^{\min }B$ is a product ideal if either $A$ is exact or $B$ is nuc…