{"paper":{"title":"The Essential Norm of Operators on the Bergman Space of Vector--Valued Functions on the Unit Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Brett D. Wick, Robert S. Rahm","submitted_at":"2014-07-17T19:34:53Z","abstract_excerpt":"Let $A_{\\alpha}^{p}(\\mathbb{B}^n;\\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\\mathbb{B}^n$ of $\\mathbb{C}^n$ of functions taking values in $\\mathbb{C}^d$. For $1<p<\\infty$ let $\\mathcal{T}_{p,\\alpha}$ be the algebra generated by finite sums of finite products of Toeplitz operators with bounded matrix--valued symbols (this is called the Toeplitz algebra in the case $d=1$). We show that every $S\\in \\mathcal{T}_{p,\\alpha}$ can be approximated by localized operators. This will be used to obtain several equivalent expressions for the essential norm of operators in $\\mathcal{T}_{p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4786","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"}