Original Articles

Convergence and completeness in asymmetrically normed sequence lattices

Published in: Quaestiones Mathematicae
Volume 38 , issue 1 , 2015 , pages: 73–81

DOI: 10.2989/16073606.2014.981715

Author(s): J.J. Conradie Department of Mathematics and Applied Mathematics, South Africa , M.D. Mabula Department of Mathematics and Applied Mathematics, South Africa

Keywords: Primary 46B42 , 46B45 , Secondary 46A40 , Primary 46B42 , 46B45 , Secondary 46A40

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Abstract

If (X, ∣∣ · ∣∣) is a real normed lattice, then p(x) = ∣∣x ⁺ ∣∣ defines an asymmetric norm on X . We give suffcient 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.

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