{
  "id": "math/9605214",
  "version": "v1",
  "published": "1996-05-09T00:00:00.000Z",
  "updated": "1996-05-09T00:00:00.000Z",
  "title": "1-complemented subspaces of spaces with 1-unconditional bases",
  "authors": [
    "Beata Randrianantoanina"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that if $X$ is a complex strictly monotone sequence space with $1$-unconditional basis, $Y \\subseteq X$ has no bands isometric to $\\ell_2^2$ and $Y$ is the range of norm-one projection from $X$, then $Y$ is a closed linear span a family of mutually disjoint vectors in $X$. We completely characterize $1$-complemented subspaces and norm-one projections in complex spaces $\\ell_p(\\ell_q)$ for $1 \\leq p, q < \\infty$. Finally we give a full description of the subspaces that are spanned by a family of disjointly supported vectors and which are $1$-complemented in (real or complex) Orlicz or Lorentz sequence spaces. In particular if an Orlicz or Lorentz space $X$ is not isomorphic to $\\ell_p$ for some $1 \\leq p < \\infty$ then the only subspaces of $X$ which are $1$-complemented and disjointly supported are the closed linear spans of block bases with constant coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-05-09T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B45",
      "41A65"
    ],
    "keywords": [
      "closed linear span",
      "complex strictly monotone sequence space",
      "norm-one projection",
      "lorentz sequence spaces",
      "bands isometric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math......5214R"
    }
  }
}