{"paper":{"title":"An alternative characterization of normed interpolation spaces between $\\ell^{1}$ and $\\ell^{q}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael Cwikel, Per G. Nilsson","submitted_at":"2017-11-13T19:33:17Z","abstract_excerpt":"Given a constant $q\\in(1,\\infty)$, we study the following property of a normed sequence space $E$:\n  =====================\n  If $\\left\\{ x_{n}\\right\\}_{n\\in\\mathbb{N}}$ is an element of $E$ and if $\\left\\{ y_{n}\\right\\}_{n\\in\\mathbb{N}}$ is an element of $\\ell^{q}$ such that $\\sum_{n=1}^{\\infty}\\left|x_{n}\\right|^{q}=\\sum_{n=1}^\\infty \\left|y_{n}\\right|^{q}$ and if the nonincreasing rearrangements of these two sequences satisfy $\\sum_{n=1}^{N}\\left|x_{n}^{*}\\right|^{q}\\le\\sum_{n=1}^{N}\\left|y_{n}^{*}\\right|^{q}$ for all $N\\in\\mathbb{N}$, then $\\left\\{ y_{n}\\right\\}_{n\\in\\mathbb{N}}\\in E$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04809","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"}