{"paper":{"title":"Weaving K-frames in Hilbert Spaces","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Deepshikha, Lalit K. Vashisht","submitted_at":"2017-10-26T07:16:52Z","abstract_excerpt":"Gavruta introduced $K$-frames for Hilbert spaces to study atomic systems with respect to a bounded linear operator. There are many differences between K-frames and standard frames, so we study weaving properties of K-frames. Two frames $\\{\\phi_{i}\\}_{i \\in I}$ and $\\{\\psi_{i}\\}_{i \\in I}$ for a separable Hilbert space $\\mathcal{H}$ are woven if there are positive constants $A \\leq B$ such that for every subset $\\sigma \\subset I$, the family $\\{\\phi_{i}\\}_{i \\in \\sigma} \\cup \\{\\psi_{i}\\}_{i \\in \\sigma^{c}}$ is a frame for $\\mathcal{H}$ with frame bounds $A, B$. In this paper, we present necessa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09562","kind":"arxiv","version":4},"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"}