{"paper":{"title":"Toeplitz and Asymptotic Toeplitz operators on $H^2(\\mathbb{D}^n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"Amit Maji, Jaydeb Sarkar, Srijan Sarkar","submitted_at":"2016-11-25T19:10:25Z","abstract_excerpt":"We initiate a study of asymptotic Toeplitz operators on the Hardy space $H^2(\\mathbb{D}^n)$ (over the unit polydisc $\\mathbb{D}^n$ in $\\mathbb{C}^n$). We also study the Toeplitz operators in the polydisc setting. Our main results on Toeplitz and asymptotic Toeplitz operators can be stated as follows: Let $T_{z_i}$ denote the multiplication operator on $H^2(\\mathbb{D}^n)$ by the $i^{th}$ coordinate function $z_i$, $i =1, \\ldots, n$, and let $T$ be a bounded linear operator on $H^2(\\mathbb{D}^n)$. Then the following hold:\n  (i) $T$ is a Toeplitz operator (that is, $T = P_{H^2(\\mathbb{D}^n)} M_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08558","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"}