Unbounded norm topology in Banach lattices

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2017-07-01

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Kandic, M.
Marabeh, M. A. A.
Troitsky, V. G.

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A net (x(alpha)) in a Banach lattice X is said to un-converge to a vector x if xl A parallel to vertical bar x(alpha) - x vertical bar boolean AND u parallel to -> 0 for every u is an element of 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 quaRi-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 B-x is un-complete. For a Banach lattice X, B-x is un-compact if X is an atomic KB-space. We also study un-compact operators and the relationship between un-convergence and weak*-convergence.

Subject Keywords

Applied Mathematics, Analysis

URI

https://hdl.handle.net/11511/67273

Journal

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

DOI

https://doi.org/10.1016/j.jmaa.2017.01.041

Collections

Department of Chemistry, Article

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Citation Formats

M. Kandic, M. A. A. Marabeh, and V. G. Troitsky, “Unbounded norm topology in Banach lattices,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, pp. 259–279, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67273.