The Ideal Structure of the Minimal Tensor Product of Ternary Rings of Operators
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| Title: | The Ideal Structure of the Minimal Tensor Product of Ternary Rings of Operators |
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| Authors: | Arpit Kansal, Vandana Rajpal |
| Source: | Journal of Informatics and Mathematical Sciences. 17:267-276 |
| Publication Status: | Preprint |
| Publisher Information: | RGN Publications, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA), Functional Analysis, Functional Analysis (math.FA) |
| Description: | 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 \( B \) |
| Document Type: | Article |
| ISSN: | 0975-5748 0974-875X |
| DOI: | 10.26713/jims.v17i3.3301 |
| DOI: | 10.48550/arxiv.2508.12374 |
| Access URL: | http://arxiv.org/abs/2508.12374 |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....9402734d34732f9e0895d8c36e99d24e |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | 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 \( V \otimes^{\mathrm{tmin}} B \) 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 \( B \) |
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| ISSN: | 09755748 0974875X |
| DOI: | 10.26713/jims.v17i3.3301 |