{
  "id": "1806.11436",
  "version": "v1",
  "published": "2018-06-28T01:19:40.000Z",
  "updated": "2018-06-28T01:19:40.000Z",
  "title": "Local Lidskii's theorems for unitarily invariant norms",
  "authors": [
    "Pedro Massey",
    "Noelia B. Rios",
    "Demetrio Stojanoff"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1610.02378",
  "categories": [
    "math.FA"
  ],
  "abstract": "Lidskii's additive inequalities (both for eigenvalues and singular values) can be interpreted as an explicit description of global minimizers of functions that are built on unitarily invariant norms, with domains consisting of certain orbits of matrices (under the action of the unitary group). In this paper, we show that Lidskii's inequalities actually describe all global minimizers of such functions and that local minimizers are also global minimizers. We use these results to obtain partial results related to local minimizers of generalized frame operator distances in the context of finite frame theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-28T01:19:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "15A60"
    ],
    "keywords": [
      "unitarily invariant norms",
      "local lidskiis theorems",
      "global minimizers",
      "local minimizers",
      "generalized frame operator distances"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}