{"paper":{"title":"A characterization of inner product spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"John M. Rassias, Mohammad Sal Moslehian","submitted_at":"2010-09-01T02:53:40Z","abstract_excerpt":"In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space $(X, \\|...\\|)$ is an inner product space if $$\\sum_{\\epsilon_i \\in \\{-1,1\\}} \\|x_1 + \\sum_{i=2}^k\\epsilon_ix_i\\|^2=\\sum_{\\epsilon_i \\in \\{-1,1\\}} (\\|x_1\\| + \\sum_{i=2}^k\\epsilon_i\\|x_i\\|)^2,$$ for some positive integer $k\\geq 2$ and all $x_1, ..., x_k \\in X$. Conversely, if $(X, \\|...\\|)$ is an inner product space, then the equality above holds for all $k\\geq 2$ and all $x_1, ..., x_k \\in X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0079","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"}