{
  "id": "1208.2072",
  "version": "v2",
  "published": "2012-08-10T01:40:43.000Z",
  "updated": "2014-06-19T18:09:23.000Z",
  "title": "$p$-Operator space structure on Feichtinger--Figà-Talamanca--Herz Segal algebras",
  "authors": [
    "Serap Öztop",
    "Nico Spronk"
  ],
  "comment": "25 pages, some arguments simplified and improved",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We consider the minimal boundedly-translation-invariant Segal algebra $S_0^p(G)$ in the Fig\\`{a}-Talamanca--Herz algebra $A_p(G)$ of a locally compact group $G$. In the case that $p=2$ and $G$ is abelian this is the classical Segal algebra of Feichtinger. Hence we call this the Feichtinger--Fig\\`{a}-Talamanca--Herz Segal algebra of $G$. Remarkably, this space is also a Segal algebra in $L^1(G)$ and is, in fact, the minimal such algebra which is closed under pointwise multiplication by $\\apg$. Even for $p=2$, this result is new for non-abelian $G$. We place a $p$-operator space structure on $S_0^p(G)$, and demonstrate the naturality of this by showing that it satisfies all natural functiorial properties: projective tensor products, restriction to subgroups and averaging over normal subgroups. However, due to complications arising within the theory of $p$-operator spaces, we are forced to work with weakly completely bounded maps in many of our results.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-19T18:09:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A15",
      "47L25",
      "22D12",
      "46J10",
      "47L50"
    ],
    "keywords": [
      "operator space structure",
      "feichtinger-figà-talamanca-herz segal algebras",
      "minimal boundedly-translation-invariant segal algebra",
      "natural functiorial properties",
      "classical segal algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2072O"
    }
  }
}