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arXiv · 1609.05301

Unbounded $p$-convergence in Lattice-Normed Vector Lattices

A. Aydın·E. Yu. Emelyanov·N. Erkurşun Özcan·M. A. A. Marabeh
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Abstract

A net $x_\alpha$ in a lattice-normed vector lattice $(X,p,E)$ is unbounded $p$-convergent to $x\in X$ if $p(|x_\alpha-x|\wedge u)\xrightarrow{o} 0$ for every $u\in X_+$. This convergence has been investigated recently for $(X,p,E)=(X,\lvert\cdot \rvert,X)$ under the name of $uo$-convergence, for $(X,p,E)=(X,\lVert\cdot\rVert,{\mathbb R})$ under the name of $un$-convergence, and also for $(X,p,{\mathbb R}^{X^*})$, where $p(x)[f]:=|f|(|x|)$, under the name $uaw$-convergence. In this paper we study general properties of the unbounded $p$-convergence.

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BibTeXRIS

A. Aydın, E. Yu. Emelyanov, N. Erkurşun Özcan, M. A. A. Marabeh. 2016-09-17. Unbounded $p$-convergence in Lattice-Normed Vector Lattices. https://arxiv.org/abs/1609.05301

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