Locally solid convergence structures
Functional Analysis
2024-04-25 v1
Abstract
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of convergence structures, we develop a theory of locally solid convergences, which generalize locally solid topologies but also includes many important non-topological convergences on a vector lattice. We consider some natural modifications of such structures: unbounded, bounded, and Choquet. We also study some specific convergences in vector lattices from the perspective of locally solid convergence structures.
Cite
@article{arxiv.2404.15641,
title = {Locally solid convergence structures},
author = {E. Bilokopytov and J. Conradie and V. G. Troitsky and J. H. van der Walt},
journal= {arXiv preprint arXiv:2404.15641},
year = {2024}
}
Comments
71 pages