{"paper":{"title":"A New Necessary Condition for the Hyponormality of Toeplitz Operators on the Bergman Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Raul E. Curto, Zeljko Cuckovic","submitted_at":"2016-10-30T02:47:41Z","abstract_excerpt":"A well known result of C. Cowen states that, for a symbol $\\varphi \\in L^{\\infty }, \\; \\varphi \\equiv \\bar{f}+g \\;\\;(f,g\\in H^{2})$, the Toeplitz operator $T_{\\varphi }$ acting on the Hardy space of the unit circle is hyponormal if and only if $f=c+T_{\\bar{h}}g,$ for some $c\\in {\\mathbb C}$, $h\\in H^{\\infty }$, $\\left\\| h\\right\\| _{\\infty}\\leq 1.$ \\ In this note we consider possible versions of this result in the {\\it Bergman} space case. \\ Concretely, we consider Toeplitz operators on the Bergman space of the unit disk, with symbols of the form $$\\varphi \\equiv \\alpha z^n+\\beta z^m +\\gamma \\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09596","kind":"arxiv","version":2},"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"}