Completeness of unbounded convergences
Copyright policy )Completeness of unbounded convergences
As a generalization of almost everywhere convergence to vector lattices, unbounded order convergence has garnered much attention. The concept of boundedly uo-complete Banach lattices was introduced by N. Gao and F. Xanthos, and has been studied in recent papers by D. Leung, V.G. Troitsky, and the aforementioned authors. We will prove that a Banach lattice is boundedly uo-complete iff it is monotonically complete. Afterwards, we study completeness-type properties of minimal topologies; minimal topologies are exactly the Hausdorff locally solid topologies in which uo-convergence implies topological convergence.
15 pages
- University of Alberta Canada
Banach lattices, boundedly \(uo\)-complete, minimal topology, Functional Analysis (math.FA), Mathematics - Functional Analysis, monotonically complete, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), completeness, FOS: Mathematics, unbounded topology, Ordered topological linear spaces, vector lattices, \(uo\)-convergence
Banach lattices, boundedly \(uo\)-complete, minimal topology, Functional Analysis (math.FA), Mathematics - Functional Analysis, monotonically complete, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), completeness, FOS: Mathematics, unbounded topology, Ordered topological linear spaces, vector lattices, \(uo\)-convergence
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