{
  "id": "2005.00075",
  "version": "v1",
  "published": "2020-04-30T19:50:00.000Z",
  "updated": "2020-04-30T19:50:00.000Z",
  "title": "Functional models up to similarity and $a$-contractions",
  "authors": [
    "Luciano Abadias",
    "Glenier Bello",
    "Dmitry Yakubovich"
  ],
  "comment": "26 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the generalization of $m$-isometries and $m$-contractions (for positive integers $m$) to what we call $a$-isometries and $a$-contractions for positive real numbers $a$. We show that any Hilbert space operator, satisfying an inequality of certain class (in hereditary form), is similar to $a$-contractions. This result is based on some Banach algebras techniques and is an improvement of a recent result by the last two authors. We also prove that any $a$-contraction $T$ is a $b$-contraction, if $b<a$ and one imposes an additional condition on the growth of the norms of $T^n x$, where $x$ is an arbitrary vector. Here we use some properties of fractional finite differences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-30T19:50:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "contraction",
      "functional models",
      "similarity",
      "fractional finite differences",
      "banach algebras techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}