2020/04/10 by Aydın, Abdullah, Emelyanov, Eduard, Gorokhova, Svetlana · 2 citations
#46A40 #46B42 #46H99 #46J40 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2004.04879
The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications of a full convergence \mathbbc on a Riesz space. The first one produces a sequential convergence \mathbbsc. The second makes an absolute \mathbbc-convergence and generalizes the absolute weak convergence. The third modification makes an unbounded \mathbbc-convergence and generalizes various unbounded convergences recently studied in the literature. The last one is applicable whenever \mathbbc is a full convergence on a commutative l-algebra and produces the multiplicative modification \mathbbmc of \mathbbc. We study general properties of full lattice convergence with emphasis on universally complete Riesz spaces and on Archimedean f-algebras. The technique and results in this paper unify and extend those which were developed and obtained in recent literature on unbounded convergences.