{"paper":{"title":"An operator extension of the parallelogram law and related norm inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Mohammad Sal Moslehian","submitted_at":"2010-11-30T16:50:40Z","abstract_excerpt":"We establish a general operator parallelogram law concerning a characterization of inner product spaces, get an operator extension of Bohr's inequality and present several norm inequalities. More precisely, let ${\\mathfrak A}$ be a $C^*$-algebra, $T$ be a locally compact Hausdorff space equipped with a Radon measure $\\mu$ and let $(A_t)_{t\\in T}$ be a continuous field of operators in ${\\mathfrak A}$ such that the function $t \\mapsto A_t$ is norm continuous on $T$ and the function $t \\mapsto \\|A_t\\|$ is integrable. If $\\alpha: T \\times T \\to \\mathbb{C}$ is a measurable function such that $\\bar{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6605","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"}