{
  "id": "2008.06769",
  "version": "v1",
  "published": "2020-08-15T19:26:22.000Z",
  "updated": "2020-08-15T19:26:22.000Z",
  "title": "Ball proximinality of $M$-ideals of compact operators",
  "authors": [
    "C. R. Jayanarayanan",
    "Sreejith Siju"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we prove the proximinality of closed unit ball of $M$-ideals of compact operators. We also prove the ball proximinality of $M$-embedded spaces in their biduals. Moreover, we show that $\\mathcal{K}(\\ell_1)$, the space of compact operators on $\\ell_1$, is ball proximinal in $\\mathcal{B}(\\ell_1)$, the space of bounded operators on $\\ell_1$, even though $\\mathcal{K}(\\ell_1)$ is not an $M$-ideal in $\\mathcal{B}(\\ell_1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-15T19:26:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L05",
      "41A50",
      "47B07",
      "47A58",
      "46B20"
    ],
    "keywords": [
      "compact operators",
      "ball proximinality",
      "closed unit ball",
      "embedded spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}