$uτ$-Convergence in locally solid vector lattices
Year: 2017
Type: preprint
Abstract: Let $x_α$ be a net in a locally solid vector lattice $(X,τ)$; we say that $x_α$ is unbounded $τ$-convergent to a vector $x\in X$ if $\lvert x_α-x \rvert\wedge w \xrightarrowτ 0$ for all $w\in X_+$. In this paper, we study general properties of unbounded $τ$-convergence (shortly, $uτ$-convergence). $uτ$-Convergence generalizes unbounded norm convergence and unbounded absolute weak convergence in normed lattices that have been investigated recently. Besides, we introduce $uτ$-topology and study briefly metrizabililty and completeness of this topology.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394665104