{"paper":{"title":"Unitarily invariant norm inequalities involving $G_1$ operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad","submitted_at":"2018-01-09T13:47:49Z","abstract_excerpt":"In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove \\begin{align*} \\|f(A)Xg(B)\\pm g(B)Xf(A)\\|_2\\leq \\left\\|\\frac{(I+|A|)X(I+|B|)+(I+|B|)X(I+|A|)}{d_Ad_B}\\right\\|_2, \\end{align*} where $A, B, X\\in\\mathbb{M}_n$ such that $A$, $B$ are Hermitian with $\\sigma (A)\\cup\\sigma(B)\\subset\\mathbb{D}$ and $f, g$ are analytic on the complex unit disk $\\mathbb{{D}}$, $g(0)=f(0)=1$, $\\textrm{Re}(f)>0$ and $\\textrm{Re}(g)>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02934","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}