{"paper":{"title":"Toeplitz operators on pluriharmonic function spaces: Deformation quantization and spectral theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Robert Fulsche","submitted_at":"2019-01-09T09:15:58Z","abstract_excerpt":"Quantization and spectral properties of Toeplitz operators acting on spaces of pluriharmonic functions over bounded symmetric domains and $\\mathbb C^n$ are discussed. Results are presented on the asymptotics \\begin{align*} \\| T_f^\\lambda\\|_\\lambda &\\to \\| f\\|_\\infty\\\\ \\| T_f^\\lambda T_g^\\lambda - T_{fg}^\\lambda\\|_\\lambda &\\to 0\\\\ \\| \\frac{\\lambda}{i} [T_f^\\lambda, T_g^\\lambda] - T_{\\{f,g\\}}^\\lambda\\|_\\lambda &\\to 0 \\end{align*} for $\\lambda \\to \\infty$, where the symbols $f$ and $g$ are from suitable function spaces. Further, results on the essential spectrum of such Toeplitz operators with ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02644","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"}