{"paper":{"title":"On left democracy function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"P. Wojtaszczyk","submitted_at":"2013-03-20T15:58:25Z","abstract_excerpt":"We continue the study undertaken in \\cite{GHN} of left democracy function $h_l(N)=\\inf_{#\\Lambda=N}\\left\\|\\sum_{n\\in \\Lambda_N} x_n\\right\\| $ of an unconditional basis in a Banach space $X$. We provide an example of a basis with $h_l$ non-doubling. Then we show that for bases with non-doubling $h_l$ the greedy projection is not optimal. Together with results from \\cite{GHN} and improved by C. Cabrelli, G. Garrig\\'os, E. Hernandez and U. Molter we get that the basis is greedy if and only if the greedy projection is optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4972","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"}