{"paper":{"title":"Sur quelques extensions au cadre Banachique de la notion d'op\\'erateur de Hilbert-Schmidt","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bernhard Hermann Haak (IMB), Jean Esterle (IMB), Said Amana Abdillah","submitted_at":"2014-06-29T19:42:58Z","abstract_excerpt":"In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operators: $p$-summing operators, $\\gamma$-summing or $\\gamma$-radonifying operators, weakly $*1$-nuclear operators and classes of operators defined via factorization properties. We introduce the class $PS_2(E; F)$ of pre-Hilbert-Schmidt operators as the class of all operators $u:E\\to F$ such that $w\\circ u \\circ v$ is Hilbert-Schmidt for every bounded operator $v: H_1\\to E$ and every bounded operator $w:F\\to H_2$, where $H_1$ et $H_2$ are Hilbert spaces. Besides the trivial case where "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7546","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"}