{"paper":{"title":"Characterizations of norm--parallelism in spaces of continuous functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ali Zamani","submitted_at":"2018-07-10T09:39:56Z","abstract_excerpt":"In this paper, we consider the characterization of norm--parallelism problem in some classical Banach spaces. In particular, for two continuous functions $f, g$ on a compact Hausdorff space $K$, we show that $f$ is norm--parallel to $g$ if and only if there exists a probability measure (i.e. positive and of full measure equal to $1$) $\\mu$ with its support contained in the norm attaining set $\\{x\\in K: \\, |f(x)| = \\|f\\|\\}$ such that $\\big|\\int_K \\overline{f(x)}g(x)d\\mu(x)\\big| = \\|f\\|\\,\\|g\\|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03780","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"}