{"paper":{"title":"$\\mathfrak{K}$-families and CPD-H-extendable families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Harsh Trivedi, Santanu Dey","submitted_at":"2014-09-12T06:31:09Z","abstract_excerpt":"We introduce, for any set $S$, the concept of $\\mathfrak{K}$-family between two Hilbert $C^*$-modules over two $C^*$-algebras, for a given completely positive definite (CPD-) kernel $\\mathfrak{K}$ over $S$ between those $C^*$-algebras and obtain a factorization theorem for such $\\mathfrak{K}$-families. If $\\mathfrak{K}$ is a CPD-kernel and $E$ is a full Hilbert $C^*$-module, then any $\\mathfrak{K}$-family which is covariant with respect to a dynamical system $(G,\\eta,E)$ on $E$, extends to a $\\tilde{\\mathfrak{K}}$-family on the crossed product $E \\times_\\eta G$, where $\\tilde{\\mathfrak{K}}$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3655","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"}