{"paper":{"title":"Unbounded $p$-convergence in Lattice-Normed Vector Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Ayd{\\i}n, E.Yu. Emelyanov, M.A.A. Marabeh, N. Erkur\\c{s}un \\\"Ozcan","submitted_at":"2016-09-17T08:53:18Z","abstract_excerpt":"A net $x_\\alpha$ in a lattice-normed vector lattice $(X,p,E)$ is unbounded $p$-convergent to $x\\in X$ if $p(|x_\\alpha-x|\\wedge u)\\xrightarrow{o} 0$ for every $u\\in X_+$. This convergence has been investigated recently for $(X,p,E)=(X,\\lvert\\cdot \\rvert,X)$ under the name of $uo$-convergence, for $(X,p,E)=(X,\\lVert\\cdot\\rVert,{\\mathbb R})$ under the name of $un$-convergence, and also for $(X,p,{\\mathbb R}^{X^*})$, where $p(x)[f]:=|f|(|x|)$, under the name $uaw$-convergence. In this paper we study general properties of the unbounded $p$-convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05301","kind":"arxiv","version":3},"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"}