{"paper":{"title":"On two refinements of the bounded weak approximate identities","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Fozouni, Raziyeh Farrokhzad","submitted_at":"2015-07-21T15:59:45Z","abstract_excerpt":"Let $A$ be a commutative Banach algebra with non-empty character space $\\Delta(A)$. In this paper, we change the concepts of convergence and boundedness in the classical notion of bounded approximate identity. This work give us a new kind of approximate identity between bounded approximate identity and bounded weak approximate identity. More precisely, a net $\\{e_{\\alpha}\\}$ in $A$ is a \\emph{c-w approximate identity} if for each $a\\in A$, the Gel'fand transform of $e_{\\alpha}a$ tends to the Gel'fand transform of $a$ in the compact-open topology and we say $\\{e_{\\alpha}\\}$ is \\emph{weakly boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05884","kind":"arxiv","version":3},"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"}