Unbounded topologies and uo-convergence in locally solid vector lattices

2017/06/06 by Taylor, Mitchell A. · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1706.01575

Abstract

Suppose X is a vector lattice and there is a notion of convergence x_α → x in X. Then we can speak of an "unbounded" version of this convergence by saying that (x_α) unbounded converges to x∈ X if | x_α-x| \wedge u→ 0 for every u ∈ X₊. In the literature, the unbounded versions of the norm, order and absolute weak convergence have been studied. Here we create a general theory of unbounded convergence but with a focus on uo-convergence and those convergences deriving from locally solid topologies.

Cited by

• Bourgain-uo sequential completeness in vector lattices
• Strong completeness of Lp-type vector lattices

Related

• uτ-Convergence in locally solid vector lattices
• Locally solid convergence structures
• Lattice uniformities inducing unbounded convergence
• Unbounded p_τ-Convergence in Vector Lattices Normed by Locally Solid Lattices
• Completeness of Unbounded Convergences