{"paper":{"title":"Toeplitz Quantization on Fock Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lewis Coburn, Raffael Hagger, Wolfram Bauer","submitted_at":"2017-04-19T08:46:21Z","abstract_excerpt":"For Toeplitz operators $T_f^{(t)}$ acting on the weighted Fock space $H_t^2$, we consider the semi-commutator $T_f^{(t)}T_g^{(t)}-T_{fg}^{(t)}$, where $t>0$ is a certain weight parameter that may be interpreted as Planck's constant $\\hbar$ in Rieffel's deformation quantization. In particular, we are interested in the semi-classical limit \\tag{$*$}\\lim\\limits_{t\\to 0}\\|T_f^{(t)}T_g^{(t)}-T_{fg}^{(t)}\\|_t. It is well-known that $\\|T_f^{(t)}T_g^{(t)}-T_{fg}^{(t)}\\|_t$ tends to $0$ under certain smoothness assumptions imposed on $f$ and $g$. This result was extended to $f,g \\in \\mathrm{BUC}(\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05652","kind":"arxiv","version":3},"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"}