{"paper":{"title":"Unbounded norm topology beyond normed lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"H. Li, M. Kandi\\'c, V.G. Troitsky","submitted_at":"2017-03-30T19:57:30Z","abstract_excerpt":"In this paper, we generalize the concept of unbounded norm (un) convergence: let $X$ be a normed lattice and $Y$ a vector lattice such that $X$ is an order dense ideal in $Y$; we say that a net $(y_\\alpha)$ un-converges to $y$ in $Y$ with respect to $X$ if $\\Bigl\\lVert\\lvert y_\\alpha-y\\rvert \\wedge x\\Bigr\\rVert\\to 0$ for every $x\\in X_+$. We extend several known results about un-convergence and un-topology to this new setting. We consider the special case when $Y$ is the universal completion of $X$. If $Y=L_0(\\mu)$, the space of all $\\mu$-measurable functions, and $X$ is an order continuous Ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10654","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"}