{
  "id": "2407.13861",
  "version": "v1",
  "published": "2024-07-18T19:03:43.000Z",
  "updated": "2024-07-18T19:03:43.000Z",
  "title": "On the reduction of powers of self-adjoint operators",
  "authors": [
    "Salima Kebli",
    "Mohammed Hichem Mortad"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $T\\in B(H)$ be such that $T^n$ is self-adjoint for some $n\\in\\mathbb{N}$ with $n\\geq 3$. The paper's primary aim is to establish the conditions that lead to the self-adjointness of $T$. We pay particular attention to the case where $T^3=0$ and how it implies $T$ is complex symmetric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-18T19:03:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-adjoint operators",
      "papers primary aim",
      "complex symmetric",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}