{
  "id": "1905.05552",
  "version": "v1",
  "published": "2019-05-14T12:31:05.000Z",
  "updated": "2019-05-14T12:31:05.000Z",
  "title": "On left $φ$-biprojectivity and left $φ$-biflatness of certain Banach algebras",
  "authors": [
    "Amir Sahami"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we study left $\\phi$-biflatness and left $\\phi$-biprojectivity of some Banach algebras, where $\\phi$ is a non-zero multiplicative linear function. We show that if the Banach algebra $A^{**}$ is left $\\phi$-biprojective, then $A$ is left $\\phi$-biflat. Using this tool we study left $\\phi$-biflatness of some matrix algebras. We also study left $\\phi$-biflatness and left $\\phi$-biprojectivity of the projective tensor product of some Banach algebras. We prove that for a locally compact group $G$, $M(G)\\otimes_{p} A(G)$ is left $\\phi\\otimes \\psi$-biprojective if and only if $G$ is finite. We show that $M(G)\\otimes_{p} L^1(G)$ is left $\\phi\\otimes \\psi$-biprojective if and only if $G$ is compact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-14T12:31:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46M10",
      "46H05",
      "43A07",
      "43A20"
    ],
    "keywords": [
      "banach algebra",
      "biflatness",
      "biprojectivity",
      "study left",
      "non-zero multiplicative linear function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}