{
  "id": "1011.0762",
  "version": "v1",
  "published": "2010-11-02T22:15:08.000Z",
  "updated": "2010-11-02T22:15:08.000Z",
  "title": "Arens Regularity of Tensor Products and Weak Amenability of Banach Algebras",
  "authors": [
    "Kazem Haghnejad Azar"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this note, we study the Arens regularity of projective tensor product $A\\hat{\\otimes}B$ whenever $A$ and $B$ are Arens regular. We establish some new conditions for showing that the Banach algebras $A$ and $B$ are Arens regular if and only if $A\\hat{\\otimes}B$ is Arens regular. We also introduce some new concepts as left-weak$^*$-weak convergence property [$Lw^*wc-$property] and right-weak$^*$-weak convergence property [$Rw^*wc-$property] and for Banach algebra $A$, suppose that $A^*$ and $A^{**}$, respectively, have $Rw^*wc-$property and $Lw^*wc-$property. Then if $A^{**}$ is weakly amenable, it follows that $A$ is weakly amenable. We also offer some results concerning the relation between these properties with some special derivation $D:A\\rightarrow A^*$. We obtain some conclusions in the Arens regularity of Banach algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-02T22:15:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach algebra",
      "arens regularity",
      "weak amenability",
      "weak convergence property",
      "projective tensor product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0762H"
    }
  }
}