{"paper":{"title":"Weak-2-local isometries on uniform algebras and Lipschitz algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Antonio M. Peralta, Lei Li, Liguang Wang, Ya-Shu Wang","submitted_at":"2017-05-10T06:35:36Z","abstract_excerpt":"We establish spherical variants of the Gleason-Kahane-Zelazko and Kowalski-S{\\l}odkowski theorems, and we apply them to prove that every weak-2-local isometry between two uniform algebras is a linear map. Among the consequences, we solve a couple of problems posed by O. Hatori, T. Miura, H. Oka and H. Takagi in 2007.\n  Another application is given in the setting of weak-2-local isometries between Lipschitz algebras by showing that given two metric spaces $E$ and $F$ such that the set Iso$((\\hbox{Lip}(E),\\|.\\|),(\\hbox{Lip}(F),\\|.\\|))$ is canonical, then every\\hyphenation{every} weak-2-local Iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03619","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"}