{"paper":{"title":"Series expansions in Fr\\'echet spaces and their duals; construction of Fr\\'echet frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Diana T. Stoeva, Stevan Pilipovi\\'c","submitted_at":"2008-09-26T14:35:54Z","abstract_excerpt":"Frames for Fr\\'echet spaces $X_F$ with respect to Fr\\'echet sequence spaces $\\Theta_F$ are studied and conditions, implying series expansions in $X_F$ and $X_F^*$, are determined. If $\\{g_i\\}$ is a $\\Theta_0$-frame for $X_0$, we construct a sequence $\\{X_s\\}_{s\\in {\\mathbb N}_0}$, $X_s\\subset X_{s-1}$, $s\\in {\\mathbb N}$, for given $\\Theta_F$, respectively a sequence $\\{\\Theta_s\\}_{s\\in {\\mathbb N}_0}$, $\\Theta_s\\subset \\Theta_{s-1}$, $s\\in {\\mathbb N}$, for given $X_F$, so that $\\{g_i\\}$ is a pre-$F$-frame (or $F$-frame) for $X_F$ with respect to $\\Theta_F$ under different assumptions given o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4647","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"}