{"paper":{"title":"Entropy numbers of embeddings of Schatten classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Aicke Hinrichs, Jan Vybiral, Joscha Prochno","submitted_at":"2016-12-23T21:31:20Z","abstract_excerpt":"Let $0<p,q \\leq \\infty$ and denote by $\\mathcal S_p^N$ and $\\mathcal S_q^N$ the corresponding finite-dimensional Schatten classes. We prove optimal bounds, up to constants only depending on $p$ and $q$, for the entropy numbers of natural embeddings between $\\mathcal S_p^N$ and $\\mathcal S_q^N$. This complements the known results in the classical setting of natural embeddings between finite-dimensional $\\ell_p$ spaces due to Sch\\\"utt, Edmunds-Triebel, Triebel and Gu\\'edon-Litvak/K\\\"uhn. We present a rather short proof that uses all the known techniques as well as a constructive proof of the upp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08105","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"}