Convergence and completeness in asymmetrically normed sequence lattices

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.