{"paper":{"title":"A Systematic Study of Frame Sequence Operators and their Pseudoinverses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"M. A. El-Gebeily, P. Balazs","submitted_at":"2008-02-25T10:49:08Z","abstract_excerpt":"In this note we investigate the operators associated with frame sequences in a Hilbert space $H$, i.e., the synthesis operator $T:\\ell ^{2}(\\mathbb{N}) \\to H$, the analysis operator $T^{\\ast}:H\\to $ $% \\ell ^{2}(\\mathbb{N}) $ and the associated frame operator $S=TT^{\\ast}$ as operators defined on (or to) the whole space rather than on subspaces. Furthermore, the projection $P$ onto the range of $T$, the projection $Q$ onto the range of $T^{\\ast}$ and the Gram matrix $G=T^{\\ast}T$ are investigated. For all these operators, we investigate their pseudoinverses, how they interact with each other, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3589","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"}