Continuous maps on ideal spaces of \(C^*\)-algebras (Q5940620)

The set \(ZI_n(A)\) of norm-closed ideals in a \(C^*\)-algebra \(A\) possesses a natural topological structure the restriction of which to the subset \(\text{Prim}(A)\) of primitive ideals of \(A\) coincides with the Jacobson topology. The author shows that, for \(C^*\)-algebras \(A\) and \(B\), continuous maps from \(\text{Prim}(A)\) to \(\text{Prim}(A)\) extend to continuous maps from \(ZI_n(A)\) to \(ZI_n(B)\). He exploits this fact to prove results about the spaces of norm-closed ideals in various tensor products of two \(C^*\)-algebras, and about the tensor products of continuous \(C^*\)-bundles.