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Convergence and completeness in asymmetrically normed sequence lattices. (English) Zbl 1426.46013

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
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