{"paper":{"title":"Unconditional structures of translates for $L_p(R^d)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Zs\\'ak, D. Freeman, E. Odell, Th. Schlumprecht","submitted_at":"2012-09-20T19:13:28Z","abstract_excerpt":"We prove that a sequence $(f_i)_{i=1}^\\infty$ of translates of a fixed $f\\in L_p(R)$ cannot be an unconditional basis of $L_p(R)$ for any $1\\le p<\\infty$. In contrast to this, for every $2<p<\\infty$, $d\\in N$ and unbounded sequence $(\\lambda_n)_{n\\in N}\\subset R^d$ we establish the existence of a function $f\\in L_p(R^d)$ and sequence $(g^*_n)_{n\\in N}\\subset L_p^*(R^d)$ such that $(T_{\\lambda_n} f, g^*_n)_{n\\in N}$ forms an unconditional Schauder frame for $L_p(R^d)$. In particular, there exists a Schauder frame of integer translates for $L_p(R)$ if (and only if) $2<p<\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4619","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"}