{
  "id": "2208.14605",
  "version": "v1",
  "published": "2022-08-31T02:49:42.000Z",
  "updated": "2022-08-31T02:49:42.000Z",
  "title": "Representations of $(A,B)$ C*-correspondences",
  "authors": [
    "Alonso Delfín"
  ],
  "comment": "AMSLaTeX; 17 pages",
  "categories": [
    "math.OA",
    "math.FA"
  ],
  "abstract": "We study representations of Hilbert bimodules on pairs of Hilbert spaces. If $A$ is a C*-algebra and $\\mathsf{X}$ is a right Hilbert $A$-module, we use such representations to faithfully represent the C*-algebras $\\mathcal{K}_A(\\mathsf{X})$ and $\\mathcal{L}_A(\\mathsf{X})$. We then extend this theory to define and prove the existence of representations of C*-correspondences on a pair of Hilbert spaces. As an application of such representations, we give necessary and sufficient conditions on an $(A,B)$ C*-correspondences to admit a Hilbert $A$-$B$-bimodule structure. Finally, we show how to represent the interior tensor product of two C*-correspondences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-31T02:49:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L08"
    ],
    "keywords": [
      "hilbert spaces",
      "interior tensor product",
      "hilbert bimodules",
      "study representations",
      "right hilbert"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}