uτ-Convergence in locally solid vector lattices

2017/06/06 by Dabboorasad, Y. A., Emelyanov, E. Yu., Marabeh, M. A. A. · 1 citation
#46A16 #46A40 (Primary). 32F45 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1706.02006

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∈ X if | x_α-x |\wedge w \xrightarrowτ 0 for all w∈ 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.

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• Strong completeness of Lp-type vector lattices

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