Article

Acta Mathematica Hungarica

, Volume 139, Issue 1, pp 147-159

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

  • J. J. ConradieAffiliated withDepartment of Mathematics and Applied Mathematics, University of the Cape Town
  • , M. D. MabulaAffiliated withDepartment of Mathematics and Applied Mathematics, University of the Cape Town Email author 

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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=ℝ m . These results enable us to prove the left-K-sequential completeness of the asymmetrically normed lattices ℝ m , C(Ω), c 0, and  p (1≦p<∞).

Key words and phrases

asymmetrically normed lattice left-K-sequential completeness

Mathematics Subject Classification

46B42 46B45 46A40