Functiones et Approximatio Commentarii Mathematici

On infinite sums of closed ideals in $F}-lattices

Lech Drewnowski

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The main result of the paper is that if $(I_n)$ is a sequence of closed ideals in an $F$-lattice $E$, then also $\sum_{n=1}^\infty I_n$, the set of all elements $x\in E$ of the form $x=\sum_n x_n$, where $x_n\in I_n$ for every $n$, is a closed ideal in $E$.

Article information

Funct. Approx. Comment. Math., Volume 44, Number 2 (2011), 279-284.

First available in Project Euclid: 22 June 2011

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Zentralblatt MATH identifier

Primary: 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 46A40: Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42] 46B42: Banach lattices [See also 46A40, 46B40]

$F$-latices closed ideals infinite sums of ideals


Drewnowski, Lech. On infinite sums of closed ideals in $F}-lattices. Funct. Approx. Comment. Math. 44 (2011), no. 2, 279--284. doi:10.7169/facm/1308749131.

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