{"paper":{"title":"Trees in renorming theory","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Richard Haydon","submitted_at":"1995-09-27T00:00:00Z","abstract_excerpt":"Trees are very agreeable objects to work with, offering a diversity of behaviour within a structure that is sufficiently simple to admit precise analysis. Thus we are able to offer fairly satisfactory necessary and sufficient conditions on a tree $\\Upsilon $ for the existence of equivalent LUR or strictly convex norms on $\\C_0(\\Upsilon )$ and for norms with the Kadec Property. In particular, we show that for a {\\sl finitely branching} tree $\\Upsilon $ the space $\\C_0(\\Upsilon )$ admits a Kadec renorming. Since some finitely branching trees fail the condition for strictly convex renormability, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9509217","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"}