{
  "abstract": "Let $A$ and $B$ be strongly Morita equivalent $C^*$-algebras, implemented by a nonzero imprimitivity bimodule $X={}_AX_B$ with its canonical operator-space structure. Denote by $Z_X$ their common multiplier centre, canonically identified through $X$. The coefficient action gives a complete contraction $Θ_X:A\\otimes_{Z_X,h}B\\to\\operatorname{CB}(X)$, where $A\\otimes_{Z_X,h}B$ is the central Haagerup tensor product obtained by balancing over $Z_X$ and $\\operatorname{CB}(X)$ is the space of completely bounded maps on $X$. We show that $Θ_X$ is injective exactly when every Glimm ideal of $A$ is $2$-primal, and isometric, equivalently completely isometric, exactly when every such ideal is primal. For each positive integer $\\ell$, norm preservation for sums of at most $\\ell$ elementary tensors is equivalent to $(\\ell^2+1)$-primality of every Glimm ideal. These conditions may equivalently be imposed on $B$. This extends the corresponding theorems of Somerset and Archbold--Somerset--Timoney to imprimitivity bimodules. We also show that, after matrix stabilization, the optimal constants bounding the central Haagerup norm by the completely bounded norm coincide for $X$, $A$ and $B$, at every finite tensor length and on the completed products, and agree with the corresponding constants after compact stabilization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39241",
  "author_total": 1,
  "authors": [
    {
      "name": "Ilja Gogić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wafyex3sjjxy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39241",
  "fulltext_url": null,
  "id": "2wafyex3sjjxy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39241",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7215097119",
  "pdf_url": "https://arxiv.org/pdf/2609.39241",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wafyex3sjjxy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39241",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39241"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Central Haagerup Tensor Products and Completely Bounded Maps under Strong Morita Equivalence",
  "title_text": "Central Haagerup Tensor Products and Completely Bounded Maps under Strong Morita Equivalence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/2wafyex3sjjxy",
  "venue": "arXiv",
  "versions": []
}