{
  "annotation_id": "5fbaf87c-0cdf-47ef-ba1b-4e763399c123",
  "date_created": "2026-02-17T05:53:12.433000Z",
  "date_modified": "2026-02-17T05:53:12.433000Z",
  "file_hash": "70f07f38b525a86429904b5c8371874dd8af512d75dc6a7bcb5481f386593529",
  "private": false,
  "record": {
    "abstract": "Let $A,B\\in\\mathbb{H}_n$ and set $H=A+B$. For each integer $k\\ge 1$ define\n  $$\n  Q_k:=\\sum_{p=0}^k \\binom{k}{p} A^pB^{k-p},\n  R_k:=\\Re\\,Q_k=\\frac{Q_k+Q_k^*}{2}.\n  $$\n  Then $H^k=\\left.\\frac{d^k}{dt^k}e^{Ht}\\right|_{t=0}$ and $Q_k=\\left.\\frac{d^k}{dt^k}(e^{At}e^{Bt})\\right|_{t=0}$. We prove that, for $k=3,4,$\n  $$\n  \\lambda(H^k)\\prec_w \\sigma(Q_k).\n  $$ Equivalently, the eigenvalues of the cubic and quartic Taylor coefficients of $e^{(A+B)t}$ are weakly majorized by the singular values of the corresponding coefficients of the Golden--Thompson product $e^{At}e^{Bt}$. Our argument combines Ky Fan variational principles with explicit commutator identitiesfor $R_k-H^k$ at orders $k=3,4$, reducing the problem to the positivity of certain double-commutator trace forms tested against Ky Fan maximizing projections. We also record a general sufficient condition for higher orders based on commutator decompositions.",
    "arxiv_id": "2601.07286",
    "authors": [
      "Teng Zhang"
    ],
    "categories": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Weak majorization inequalities for the cubic and quartic coefficients of $e^{(A+B)t}$ versus $e^{At}e^{Bt}$",
    "url": "https://arxiv.org/abs/2601.07286",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "416b54e2-45d4-4093-931a-144ea6e178b8",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}