{"paper":{"title":"Resolutions of Hilbert Modules and Similarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"Ciprian Foias, Jaydeb Sarkar, Ronald G. Douglas","submitted_at":"2009-07-15T03:36:35Z","abstract_excerpt":"Let H^2_m be the Drury-Arveson (DA) module which is the reproducing kernel Hilbert space with the kernel function (z, w) \\in B^m \\times B^m \\raro (1 - <z,w>)^{-1}. We investigate for which multipliers \\theta : \\mathbb{B}^m \\raro \\cll(\\cle, \\cle_*) the quotient module \\clh_{\\theta} is similar to H^2_m \\otimes \\clf for some Hilbert space \\clf, where M_{\\theta} is the corresponding multiplication operator in \\cll(H^2_m \\otimes \\cle, H^2_m \\otimes \\cle_*) for Hilbert spaces \\cle and \\cle_* and \\clh_{\\theta} is the quotient module (H^2_m \\otimes \\cle_*)/ {clos} [M_{\\theta}(H^2_m \\otimes \\cle)]. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2487","kind":"arxiv","version":5},"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"}