{
  "id": "1806.05443",
  "version": "v1",
  "published": "2018-06-14T10:07:30.000Z",
  "updated": "2018-06-14T10:07:30.000Z",
  "title": "The absolute values and cover projections for a class of operator matrices involving idempotents",
  "authors": [
    "Yuan Li",
    "Xiaomei Cai",
    "Shuaijie Wang"
  ],
  "comment": "19",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we consider the formulas of the absolute value $|Q_{\\lambda,\\mu}|,$ where $Q_{\\lambda,\\mu} = \\left(\\begin{array}{cc}\\lambda I&P P^*&\\mu I\\end{array}\\right): \\mathcal{H} \\oplus \\mathcal{K}$ is self-adjoint operators in the Hilbert space $\\mathcal{H}\\oplus\\mathcal{K}.$ Then the positive parts and the cover projections of $Q_{\\lambda,0}$ are obtained. Also, we character the symmetry $J$ such that a projection $P$ is the $J$-projection. In particular, the minimal element of the symmetry $J$ with $JP\\geqslant0$ is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-14T10:07:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "absolute value",
      "cover projections",
      "operator matrices",
      "idempotents",
      "self-adjoint operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}