{
  "id": "1804.08446",
  "version": "v1",
  "published": "2018-04-20T09:15:59.000Z",
  "updated": "2018-04-20T09:15:59.000Z",
  "title": "Remarks on Banach spaces determined by their finite dimensional subspaces",
  "authors": [
    "Karim Khanaki"
  ],
  "comment": "The primary classification for this submission is Functional Analysis. This paper is companion-piece to arXiv:1603.08134 Comments are welcome (K.Khanaki@gmail.com)",
  "categories": [
    "math.FA",
    "math.LO"
  ],
  "abstract": "A separable Banach space $X$ is said to be finitely determined if for each separable space $Y$ such that $X$ is finitely representable (f.r.) in $Y$ and $Y$ is f.r. in $X$ then $Y$ is isometric to $X$. We provide a direct proof (without model theory) of the fact that every finitely determined space $X$ (isometrically) contains every (separable) space $Y$ which is finitely representable in $X$. We also point out how a similar argument proves the Krivine-Maurey theorem on stable Banach spaces, and give the model theoretic interpretations of some results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-20T09:15:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite dimensional subspaces",
      "model theoretic interpretations",
      "model theory",
      "stable banach spaces",
      "krivine-maurey theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}