{"paper":{"title":"Building highly conditional almost greedy and quasi-greedy bases in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Denka Kutzarova, Fernando Albiac, Jose L. Ansorena, Stephen DIlworth","submitted_at":"2018-03-21T11:41:44Z","abstract_excerpt":"It is known that for a conditional quasi-greedy basis $\\mathcal{B}$ in a Banach space $\\mathbb{X}$, the associated sequence $(k_{m}[\\mathcal{B}])_{m=1}^{\\infty}$ of its conditionality constants verifies the estimate $k_{m}[\\mathcal{B}]=\\mathcal{O}(\\log m)$ and that if the reverse inequality $\\log m =\\mathcal{O}(k_m[\\mathcal{B}])$ holds then $\\mathbb{X}$ is non-superreflexive. Indeed, it is known that a quasi-greedy basis in a superreflexive quasi-Banach space fulfils the estimate $k_{m}[\\mathcal{B}]=\\mathcal{O}(\\log m)^{1-\\epsilon}$ for some $\\epsilon>0$. However, in the existing literature on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08351","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"}