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Title: | Unbounded norm topology in Banach lattices |
Authors: | KANDIC, MARKO MARABEH, MOHAMMAD A. A. TROITSKY, VLADIMIR G. |
Keywords: | Banach lattice;un-convergence;uo-convergence;un-topology |
Issue Date: | 2017 |
Publisher: | Journal of Mathematical Analysis and Applications |
Abstract: | A net (xα) in a Banach lattice X is said to un-converge to a vector x if || |xα−x|∧u ||→0 for every u ∈X+. In this paper, we investigate un-topology, i.e., the topology that corresponds to un-convergence. We show that un-topology agrees with the norm topology iff X has a strong unit. Un-topology is metrizable iff X has a quasi-interior point. Suppose that X is order continuous, then un-topology is locally convex iff X is atomic. An order continuous Banach lattice Xis a KB-space iff its closed unit ball B_X is un-complete. For a Banach lattice X, B_X is un-compact iff X is an atomic KB-space. We also study un-compact operators and the relationship between un-convergence and weak*-convergence. |
URI: | https://scholar.ptuk.edu.ps/handle/123456789/446 |
Appears in Collections: | Applied science faculty |
Files in This Item:
File | Description | Size | Format | |
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Unbounded norm topology in Banach lattices.pdf | 358.95 kB | Adobe PDF | View/Open |
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