Conradie, J. J.; Mabula, M. D. Convergence and completeness in asymmetrically normed sequence lattices. (English) Zbl 1426.46013 Quaest. Math. 38, No. 1, 73-81 (2015). Summary: If \((X,\|\cdot\|)\) 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. MSC: 46B42 Banach lattices 46B45 Banach sequence spaces 46A40 Ordered topological linear spaces, vector lattices Keywords:asymmetrically normed lattice; left-\(K\)-sequential completeness; Smyth completeness PDFBibTeX XMLCite \textit{J. J. Conradie} and \textit{M. D. Mabula}, Quaest. Math. 38, No. 1, 73--81 (2015; Zbl 1426.46013) Full Text: DOI