{"paper":{"title":"Hilbert $C^*$-modules over $\\Sigma^*$-algebras II: $\\Sigma^*$-Morita equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Clifford A. Bearden","submitted_at":"2017-01-28T23:30:21Z","abstract_excerpt":"In previous work, we defined and studied $\\Sigma^*$-modules, a class of Hilbert $C^*$-modules over $\\Sigma^*$-algebras (the latter are $C^*$-algebras that are sequentially closed in the weak operator topology). The present work continues this study by developing the appropriate $\\Sigma^*$-algebraic analogue of the notion of strong Morita equivalence for $C^*$-algebras. We define strong $\\Sigma^*$-Morita equivalence, prove a few characterizations, look at the relationship with equivalence of categories of a certain type of Hilbert space representation, study $\\Sigma^*$-versions of the interior "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08333","kind":"arxiv","version":2},"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"}