A characterization of completeness via absolutely convergent series and the Weierstrass test in asymmetric normed semilinear spaces (Q1724479)
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scientific article; zbMATH DE number 7022682
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of completeness via absolutely convergent series and the Weierstrass test in asymmetric normed semilinear spaces |
scientific article; zbMATH DE number 7022682 |
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A characterization of completeness via absolutely convergent series and the Weierstrass test in asymmetric normed semilinear spaces (English)
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14 February 2019
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Summary: Asymmetric normed semilinear spaces are studied. A description of biBanach, left \(K\)-sequentially complete, and Smyth complete asymmetric normed semilinear spaces is provided and three appropriate notions of absolute convergence in the asymmetric normed framework are introduced. Some characterizations of completeness are also obtained via absolutely convergent series. Moreover, as an application, a Weierstrass test for the convergence of series is derived.
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