Maximal quasi-normed extension of quasi-normed lattices

Автор: Kusraev Anatoly Georgievich, Tasoev Batradz Botazovich

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.19, 2017 года.

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The purpose of this article is to extend the Abramovich's construction of a maximal normed extension of a normed lattice to quasi-Banach setting. It is proved that the maximal quasi-normed extension Xϰ of a Dedekind complete quasi-normed lattice X with the weak σ-Fatou property is a quasi-Banach lattice if and only if X is intervally complete. Moreover, Xϰ has the Fatou and the Levi property provided that X is a Dedekind complete quasi-normed space with the Fatou property. The possibility of applying this construction to the definition of a space of weakly integrable functions withrespect to a measure taking values from a quasi-Banach lattice is also discussed, since the duality based definition does not work in the quasi-Banach setting.

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Quasi-banach lattice, maximal quasi-normed extension, fatou property, levi property vector measure, space of weakly integrable functions

Короткий адрес: https://sciup.org/14318581

IDR: 14318581 | DOI: 10.23671/VNC.2017.3.7111

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