{"paper":{"title":"Numerical range of weighted composition operators which contain zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Asma Negahdari, Mahsa Fatehi","submitted_at":"2019-01-23T06:05:39Z","abstract_excerpt":"In this paper, we study when zero belongs to the numerical range of weighted composition operators $C_{\\psi,\\varphi}$ on the Fock space $\\mathcal{F}^{2}$, where $\\varphi(z)=az+b$, $a,b \\in \\mathbb{C}$ and $|a|\\leq 1$. In the case that $|a|<1$, we obtain a set contained in the numerical range of $C_{\\psi,\\varphi}$ and find the conditions under which the numerical range of $C_{\\psi,\\varphi}$ contain zero. Then for $|a|=1$, we precisely determine the numerical range of $C_{\\psi,\\varphi}$ and show that zero lies in its numerical range."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07736","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"}