{
  "id": "2108.12576",
  "version": "v1",
  "published": "2021-08-28T05:13:17.000Z",
  "updated": "2021-08-28T05:13:17.000Z",
  "title": "Birkhoff-James extensions of continuous functions on metric spaces",
  "authors": [
    "Saptak Bhattacharya"
  ],
  "comment": "9 pages, 0 figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we extend the investigations regarding Birkhoff-James orthogonality of linear operators to bounded continuous functions on metric spaces. We introduce Birkhoff-James extensions of continuous functions and study them in detail, in the separate contexts of compact and non-compact metric spaces. We conclude by discussing an application of our ideas to the study of Birkhoff-James orthogonality in $C(X)$ with the supremum norm, where $X$ is a compact metric space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-28T05:13:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A51",
      "54E45",
      "46B20"
    ],
    "keywords": [
      "continuous functions",
      "birkhoff-james extensions",
      "investigations regarding birkhoff-james orthogonality",
      "non-compact metric spaces",
      "supremum norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}