{"paper":{"title":"Decomposition of functions between Banach spaces in the orthogonality equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Maysam Maysami Sadr","submitted_at":"2016-10-03T06:45:10Z","abstract_excerpt":"Let $E,F$ be Banach spaces. In the case that $F$ is reflexive we give a description for the solutions $(f,g)$ of the Banach-orthogonality equation $$\\langle f(x),g(\\alpha)\\rangle=\\langle x,\\alpha\\rangle\\hspace{10mm}\\forall x\\in E,\\forall \\alpha\\in E^*,$$ where $f:E\\rightarrow F,g:E^*\\rightarrow F^*$ are two maps. Our result generalizes the recent result of {\\L}ukasik and W\\'{o}jcik in the case that $E$ and $F$ are Hilbert spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00423","kind":"arxiv","version":2},"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"}