{"paper":{"title":"Localization and compactness of Operators on Fock Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Brett D. Wick, Xiaofen Lv, Zhangjian Hu","submitted_at":"2017-12-20T00:40:29Z","abstract_excerpt":"For $0<p\\leq\\infty$, let $F^{p}_\\varphi$ be the Fock space induced by a weight function $\\varphi$ satisfying $ dd^c \\varphi \\simeq \\omega_0$. In this paper, given $p\\in (0, 1]$ we introduce the concept of weakly localized operators on $ F^{p}_\\varphi$, we characterize the compact operators in the algebra generated by weakly localized operators. As an application, for $0<p<\\infty$ we prove that an operator $T$ in the algebra generated by bounded Toeplitz operators with $\\textrm{BMO}$ symbols is compact on $F^p_\\varphi$ if and only if its Berezin transform satisfies certain vanishing property at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07278","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"}