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Convergence and completeness in asymmetrically normed sequence lattices


J.J. Conradie
M.D. Mabula

Abstract

If (X, ∥ · ∥) is a real normed lattice, then p(x) = ∥x+∥ defines an
asymmetric norm on X. We give sufficient conditions for (X, p) to be left-K-sequentially complete in the case where X is a normed sequence lattice and investigate the Smyth completeness of the positive cone of such lattices.

Keywords: Asymmetrically normed lattice, left-K-sequential completeness, Smyth completeness.


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eISSN: 1727-933X
print ISSN: 1607-3606