{"paper":{"title":"Cotype and summing properties in Banach spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marius Junge","submitted_at":"1993-12-22T16:45:41Z","abstract_excerpt":"It is well known in Banach space theory that for a finite dimensional space $E$ there exists a constant $c_E$, such that for all sequences $(x_k)_k \\subset E$ one has \\[ \\summ_k \\noo x_k \\rrm \\kl c_E \\pl \\sup_{\\eps_k \\pm 1} \\noo \\summ_k \\eps_k x_k \\rrm \\pl .\\] Moreover, if $E$ is of dimension $n$ the constant $c_E$ ranges between $\\sqrt{n}$ and $n$. This implies that absolute convergence and unconditional convergence only coincide in finite dimensional spaces. We will characterize Banach spaces $X$, where the constant $c_E \\sim \\sqrt{n}$ for all finite dimensional subspaces. More generally, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9312206","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"}