{
  "id": "1804.05621",
  "version": "v1",
  "published": "2018-04-16T11:52:21.000Z",
  "updated": "2018-04-16T11:52:21.000Z",
  "title": "Isometric dilations and von Neumann inequality for finite rank commuting contractions",
  "authors": [
    "Sibaprasad Barik",
    "B. Krishna Das",
    "Jaydeb Sarkar"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA",
    "math.CV",
    "math.OA"
  ],
  "abstract": "It is well known that for an arbitrary $n$-tuple of commuting contractions, $n\\geq 3$, neither the existence of isometric dilation nor the von-Neumann inequality holds. In this paper we provide an explicit isometric dilation for a large class of $n$-tuple $(n\\geq 3)$ of commuting contractions. The present class of tuples of operators is motivated by a polydisc version of commutant lifting theorem by Ball, Li, Timotin and Trent. The present class of operators is larger than the one considered in \\cite{BDHS}. Also we prove a sharper von-Neumann inequality on an algebraic variety in the closure of the polydisc in $\\mathbb{C}^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-16T11:52:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A13",
      "47A20",
      "47A56",
      "47B38",
      "14M99",
      "46E20",
      "30H10"
    ],
    "keywords": [
      "finite rank commuting contractions",
      "von neumann inequality",
      "explicit isometric dilation",
      "von-neumann inequality holds",
      "sharper von-neumann inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}