{"paper":{"title":"Reverse triangle inequality in Hilbert $C^*$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"H. Mahyar, M. Khosravi, M.S. Moslehian","submitted_at":"2009-11-14T07:57:58Z","abstract_excerpt":"We prove several versions of reverse triangle inequality in Hilbert $C^*$-modules. We show that if $e_1, ..., e_m$ are vectors in a Hilbert module ${\\mathfrak X}$ over a $C^*$-algebra ${\\mathfrak A}$ with unit 1 such that $<e_i,e_j>=0 (1\\leq i\\neq j \\leq m)$ and $\\|e_i\\|=1 (1\\leq i\\leq m)$, and also $r_k,\\rho_k\\in\\Bbb{R} (1\\leq k\\leq m)$ and $x_1, ..., x_n\\in {\\mathfrak X}$ satisfy $$0\\leq r_k^2 \\|x_j\\|\\leq {Re}< r_ke_k,x_j> ,\\quad0\\leq \\rho_k^2 \\|x_j\\| \\leq {Im}< \\rho_ke_k,x_j> ,$$ then [\\sum_{k=1}^m(r_k^2+\\rho_k^2)]^{{1/2}}\\sum_{j=1}^n \\|x_j\\|\\leq\\|\\sum_{j=1}^nx_j\\|, and the equality holds i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2751","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"}