Unbounded p_τ-Convergence in Vector Lattices Normed by Locally Solid Lattices

2017/10/31 by Aydın, Abdulla
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1711.00734

Abstract

Let (x_α) be a net in a vector lattice normed by locally solid lattice (X,p,E_τ). We say that (x_α) is unbounded p_τ-convergent to x∈ X if p(| x_α-x|\wedge u)\xrightarrowτ 0 for every u∈ X₊. This convergence has been studied recently for lattice-normed vector lattices as the up-convergence in \citeAGG,AEEM,AEEM2, the uo-convergence in \citeGTX, and, as the un-convergence in \citeDOT,GX,GTX,KMT,Tr2. In this paper, we study the general properties of the unbounded p_τ-convergence.

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