Topological properties of spaces of ideals of the minimal tensor product

الأصل · EN

One shows that for two C*-algebras A₁ and A₂ any continuous function on Prim(A₁)× Prim(A₂) can be continuously extended to Prim(A₁⊗ A₂) provided it takes its values in a T₁ topological space. This generalizes a 1977 result of L.G. Brown. A new proof is given for a result of R.J. Archbold about the space of minimal primal ideals of A₁⊗ A₂. To obtain these two results one makes use of the topological properties of the space of prime ideals of the minimal tensor product.