Ideal spaces of the Haagerup tensor product of C*-algebras

Following the work of Allen, Sinclair and Smith on the primitive ideal space of the Haagerup tensor product A ⊗_h, B of C*-algebras A and B, we investigate the hull-kernel topology and use this to determine various other ideal spaces and their topologies in relation to the corresponding ideal spaces of A and B. We study the semi-continuity of norm functions I → ∥cursive Greek chi + I∥ (cursive Greek chi ∈ A ⊗_h B) on these ideal spaces and identify the separated points of Prim(A ⊗_h B). Finally, we exhibit several conditions each of which is equivalent to the quasi-standardness of A ⊗_h B.