The Ideal Structure of the Minimal Tensor Product of Ternary Rings of Operators - Kansal, Arpit; Rajpal, Vandana (Journal of Informatics and Mathematical Sciences, 2025)
Let \(V\) be a ternary ring of operator, and let \(B\) be a \(C^*\)-algebra. We study the structure of the ideal space of the operator space injective tensor product \(V \otimes^{tmin} B\) via two maps: \begin{align*} Φ(I, J) = \ker(q_I \otimes^{tmin} q_J) \quad \text{and} \quad Δ(I, J) = I \otimes^{tmin} B + V \otimes^{tmin} J. \end{align*} We prove that \(Φ\) is continuous with respect to the hull-kernel topology, and that its restriction to primitive and prime ideals defines a homeomorphism onto dense subsets of the respective ideal spaces of \(V \otimes^{tmin} B\). We prove that if \(Φ = Δ\), then \(Φ\) induces a homeomorphism between the space of minimal primal ideals of \(V \otimes^{tmin} B\) and the product of the spaces of minimal primal ideals of \(V \) and \(B\).