The ideal structure of the minimal Tensor Product of Ternary Rings of Operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911109213061120 |
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| author | Rajpal, Vandana Kansal, Arpit |
| author_facet | Rajpal, Vandana Kansal, Arpit |
| contents | 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 \( V \otimes^{\mathrm{tmin}} B \) via two maps: \[ Φ(I, J) = \ker(q_I \otimes^{\mathrm{tmin}} q_J) \quad \text{and} \quad Δ(I, J) = I \otimes^{\mathrm{tmin}} B + V \otimes^{\mathrm{tmin}} J. \] 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 \( V \otimes^{\mathrm{tmin}} B \).
We prove that if \( Φ= Δ\), then \( Φ\) induces a homeomorphism between the space of minimal primal ideals of \( V \otimes^{\mathrm{tmin}} B \) and the product of the spaces of minimal primal ideals of \( V \) and \( B \) |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_12374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The ideal structure of the minimal Tensor Product of Ternary Rings of Operators Rajpal, Vandana Kansal, Arpit Functional Analysis Operator Algebras 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 \( V \otimes^{\mathrm{tmin}} B \) via two maps: \[ Φ(I, J) = \ker(q_I \otimes^{\mathrm{tmin}} q_J) \quad \text{and} \quad Δ(I, J) = I \otimes^{\mathrm{tmin}} B + V \otimes^{\mathrm{tmin}} J. \] 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 \( V \otimes^{\mathrm{tmin}} B \). We prove that if \( Φ= Δ\), then \( Φ\) induces a homeomorphism between the space of minimal primal ideals of \( V \otimes^{\mathrm{tmin}} B \) and the product of the spaces of minimal primal ideals of \( V \) and \( B \) |
| title | The ideal structure of the minimal Tensor Product of Ternary Rings of Operators |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2508.12374 |