Acta Mathematica Hungarica

, Volume 139, Issue 1, pp 147–159

Convergence and left-K-sequential completeness in asymmetrically normed lattices

Article

DOI: 10.1007/s10474-012-0269-5

Cite this article as:
Conradie, J.J. & Mabula, M.D. Acta Math Hung (2013) 139: 147. doi:10.1007/s10474-012-0269-5

Abstract

If (X,∥.∥) is a real normed lattice, then p(x)=∥x+∥ defines an asymmetric norm on X. We study the convergence of sequences in the asymmetrically normed lattice (X,p) and give a characterization of the set of limit points of a convergent sequence in the case X=ℝm. These results enable us to prove the left-K-sequential completeness of the asymmetrically normed lattices ℝm, C(Ω), c0, and p (1≦p<∞).

Key words and phrases

asymmetrically normed latticeleft-K-sequential completeness

Mathematics Subject Classification

46B4246B4546A40

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Applied MathematicsUniversity of the Cape TownCape TownSouth Africa