Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775034 | Journal of Mathematical Analysis and Applications | 2017 | 21 Pages |
Abstract
A net (xα) in a Banach lattice X is said to un-converge to a vector x if â|xαâx|â§uââ0 for every uâX+. 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 X is a KB-space iff its closed unit ball BX is un-complete. For a Banach lattice X, BX 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
M. KandiÄ, M.A.A. Marabeh, V.G. Troitsky,