Unbounded p-Convergence in Lattice-Normed Vector Lattices

Abstract

A net x? in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ? X if p(| x?? x| ? u) ? o 0 for every u ? X+. This convergence has been investigated recently for (X, p, E) = (X, |·|, X) under the name of uo-convergence, for (X, p, E) = (X, ?·?, ?) under the name of un-convergence, and also for (X, p, ?X ?) , where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence. © 2019, Allerton Press, Inc.