{"paper":{"title":"Schatten properties, nuclearity and minimality of shift invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Joachim Toft","submitted_at":"2016-05-10T14:59:35Z","abstract_excerpt":"We extend Feichtinger's minimality property on smallest non-trivial time-frequency shift invariant Banach spaces, to the quasi-Banach case. Analogous properties are deduced for certain matrix classes.\n  We use these results to prove that $\\operatorname{Op}(a)$ is a Schatten-$q$ operator from $M^\\infty$ to $M^p$ and $r$-nuclear operator from $M^\\infty$ to $M^r$ when $a\\in M^r$ for suitable $p$, $q$ and $r$ in $(0,\\infty ]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03042","kind":"arxiv","version":5},"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"}