{"paper":{"title":"Roots of Toeplitz Operators on the Bergman space","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Issam Louhichi, N. V. Rao","submitted_at":"2010-04-01T12:40:50Z","abstract_excerpt":"One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk $\\mathbb D$ in the complex plane $\\mathbb C$ is a complete description of the commutant of a given Toeplitz operator, that is the set of all Toeplitz operators that commute with it. In \\cite{l}, the first author obtained a complete description of the commutant of Toeplitz operator $T$ with any quasihomogeneous symbol $\\phi(r)e^{ip\\theta}, p>0$ in case it has a Toeplitz p-th root $S$ with symbol $\\psi(r)e^{i\\theta}$, namely, commutant of $T$ is the closure of the linear space generated by powe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0121","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"}