{"paper":{"title":"Geometric constructions of thin Blaschke products and reducing subspace problem","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Hansong Huang, Kunyu Guo","submitted_at":"2013-06-30T03:45:52Z","abstract_excerpt":"In this paper, we mainly study geometric constructions of thin Blaschke products $B$ and reducing subspace problem of multiplication operators induced by such symbols $B$ on the Bergman space. Considering such multiplication operators $M_B$, we present a representation of those operators commuting with both $M_B$ and $M_B^*$. It is shown that for \"most\" thin Blaschke products $B$, $M_B$ is irreducible, i.e. $M_B$ has no nontrivial reducing subspace; and such a thin Blaschke product $B$ is constructed.\n  As an application of the methods, it is proved that for \"most\" finite Blaschke products $\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0174","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"}