The ideal structure of the minimal Tensor Product of Ternary Rings of Operators

2025/08/17 by Rajpal, Vandana, Kansal, Arpit
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2508.12374

Abstract

Let \( V \) be a ternary ring of operator and \( B \) a \( C^* \)-algebra. We study the structure of the ideal space of the operator space injective tensor product \( V ⊗^tmin B \) via two maps: Φ(I, J) = ker(q_I ⊗^tmin q_J) and Δ(I, J) = I ⊗^tmin B + V ⊗^tmin J. We show 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 \( V ⊗^tmin B \). We prove that if \( Φ= Δ\), then \( Φ\) induces a homeomorphism between the space of minimal primal ideals of \( V ⊗^tmin B \) and the product of the spaces of minimal primal ideals of \( V \) and \( B \)

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