The space of ideals in the minimal tensor product of C*-algebras

Original · EN

For C*-algebras A₁, A₂ the map (I₁,I₂)→ ker(qᵢ₁⊗ qᵢ₂) from Id′(A₁)× Id′(A₂) into Id′(A₁⊗min A₂) is a homeomorphism onto its image which is dense in the range. Here, for a C*-algebra A, the space of all proper closed two sided ideals endowed with an adequate topology is denoted Id′(A) and qᵢ is the quotient map of A onto A/I. New proofs of the equivalence of the property (F) of Tomiyama for A₁⊗min A₂ with certain other properties are presented.