{"paper":{"title":"Trace ideal criteria for embeddings and composition operators on model spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Aleman, E. Malinnikova, K.-M. Perfekt, Yu. Lyubarskii","submitted_at":"2013-07-10T02:01:22Z","abstract_excerpt":"Let $K_\\theta$ be a model space generated by an inner function $\\theta$. We study the Schatten class membership of embeddings $I : K_\\theta \\to L^2(\\mu)$, $\\mu$ a positive measure, and of composition operators $C_\\phi:K_\\theta\\to H^2(\\mathbb D)$ with a holomprphic function $\\phi:\\mathbb D\\rightarrow \\mathbb D$. In the case of one-component inner functions $\\theta$ we show that the problem can be reduced to the study of natural extensions of $I$ and $C_\\phi$ to the Hardy-Smirnov space $E^2(D)$ in some domain $D\\supset \\mathbb D$. In particular, we obtain a characterization of Schatten membershi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2652","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"}