{"paper":{"title":"Diameter preserving linear bijections of $C(X)$","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lajos Molnar, M. Gyory","submitted_at":"1997-07-04T00:00:00Z","abstract_excerpt":"The aim of this paper is to solve a linear preserver problem on the function algebra $C(X)$. We show that in case $X$ is a first countable compact Hausdorff space, every linear bijection $\\phi:C(X)\\to C(X)$ having the property that $diam(\\phi(f)(X))=diam(f(X))$ $(f\\in C(X))$ is of the form \\[ \\phi(f)=\\tau \\cdot f\\circ \\varphi +t(f)1 \\qquad (f\\in C(X)) \\] where $\\tau$ is a complex number of modulus 1, $\\varphi:X\\to X$ is a homeomorphism and $t$ is a linear functional on $C(X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9707208","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"}