{"paper":{"title":"Frames and Bases in Tensor Product of Hilbert Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Amir Khosravi, Mohammad Sadegh Asgari","submitted_at":"2012-03-31T12:50:59Z","abstract_excerpt":"In this article we develop a theory for frames in tensor product of Hilbert spaces. We show that like bases if Y_1, Y_2, \\cdot \\cdot \\cdot, Y_n are frames for H_1,H_2, \\cdot \\cdot \\cdot, H_n, respectively, then Y_1\\otimesY_2\\otimes...\\otimesY_n is a frame for H_\\otimes1H_2\\otimes \\cdot \\cdot \\cdot \\otimesH_n. Moreover we consider the canonical dual frame in tensor product space. We further obtain a relation between the dual frames in Hilbert spaces, and their tensor product."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0096","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"}