{
  "id": "1609.08659",
  "version": "v1",
  "published": "2016-09-27T20:45:49.000Z",
  "updated": "2016-09-27T20:45:49.000Z",
  "title": "Tight J-frames in Krein space and the associated J-frame potential",
  "authors": [
    "Sk. Monowar Hossein",
    "Shibashis Karmakar",
    "Kallol Paul"
  ],
  "journal": "IJMA, Vol.10, 2016, no.19, 917-931",
  "doi": "10.12988/ijma.2016.6355",
  "categories": [
    "math.FA"
  ],
  "abstract": "Motivated by the idea of $J$-frame for a Krein space $\\textbf{\\textit{K}}$, introduced by Giribet \\textit{et al.} (J. I. Giribet, A. Maestripieri, F. Mart\\'inez Per\\'{i}a, P. G. Massey, \\textit{On frames for Krein spaces}, J. Math. Anal. Appl. (1), {\\bf 393} (2012), 122--137.), we introduce the notion of $\\zeta-J$-tight frame for a Krein space $\\textbf{\\textit{K}}$. In this paper we characterize $J$-orthonormal basis for $\\textbf{\\textit{K}}$ in terms of $\\zeta-J$-Parseval frame. We show that a Krein space is richly supplied with $\\zeta-J$-Parseval frames. We also provide a necessary and sufficient condition when the linear sum of two $\\zeta-J$-Parseval frames is again a $\\zeta-J$-Parseval frame. We then generalize the notion of $J$-frame potential in Krein space from Hilbert space frame theory. Finally we provided a necessary and sufficient condition for a $J$-frame potential of the corresponding $\\zeta-J$-tight frame to be minimum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-27T20:45:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "46C05",
      "46C20"
    ],
    "keywords": [
      "krein space",
      "associated j-frame potential",
      "parseval frame",
      "tight j-frames",
      "tight frame"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}