{"paper":{"title":"Landau and Gruss type inequalities for inner product type integral transformers in norm ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.OA"],"primary_cat":"math.FA","authors_text":"Danko R. Jocic, Dorde E. Krtinic, Mohammad Sal Moslehian","submitted_at":"2011-11-14T06:39:09Z","abstract_excerpt":"For a probability measure $\\mu$ and for square integrable fields $(\\mathscr{A}_t)$ and $(\\mathscr{B}_t)$ ($t\\in\\Omega$) of commuting normal operators we prove Landau type inequality\n\\llu\\int_\\Omega\\mathscr{A}_tX\\mathscr{B}_td\\mu(t)-\n   \\int_\\Omega\\mathscr{A}_t\\,d\\mu(t)X  \\int_\\Omega\\mathscr{B}_t\\,d\\mu(t) \\rru \n\\le \\llu \\sqrt{\\,\\int_\\Omega|\\mathscr{A}_t|^2\\dt-|\\int_\\Omega\\mathscr{A}_t\\dt|^2}X \\sqrt{\\,\\int_\\Omega|\\mathscr{B}_t|^2 \\dt-|\\int_\\Omega\\mathscr{B}_t\\dt|^2} \\rru\nfor all $X\\in\\mathcalb{B}(\\mathcal{H})$ and for all unitarily invariant norms $\\lluo\\cdot\\rruo$.\n  For Schatten $p$-norms simi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3112","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"}