{"paper":{"title":"Unitarily invariant norm inequalities for operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Niknam, M. Erfanian Omidvar, M.S. Moslehian","submitted_at":"2011-01-20T13:16:01Z","abstract_excerpt":"We present several operator and norm inequalities for Hilbert space operators. In particular, we prove that if $A_{1},A_{2},...,A_{n}\\in {\\mathbb B}({\\mathscr H})$, then \\[|||A_{1}A_{2}^{*}+A_{2}A_{3}^{*}+...+A_{n}A_{1}^{*}|||\\leq|||\\sum_{i=1}^{n}A_{i}A_{i}^{*}|||,\\] for all unitarily invariant norms.  We also show that if $A_{1},A_{2},A_{3},A_{4}$ are projections in ${\\mathbb B}({\\mathscr H})$, then &&|||(\\sum_{i=1}^{4}(-1)^{i+1}A_{i})\\oplus0\\oplus0\\oplus0|||&\\leq&|||(A_{1}+|A_{3}A_{1}|)\\oplus (A_{2}+|A_{4}A_{2}|)\\oplus(A_{3}+|A_{1}A_{3}|)\\oplus(A_{4}+|A_{2}A_{4}|)||| for any unitarily invari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3895","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"}