Unbounded $p_τ$-Convergence in Vector Lattices Normed by Locally Solid Lattices
Abdulla Aydın · arXiv (Cornell University) · 2017
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 $x\in X$ if $p(\lvert x_α-x\rvert\wedge u)\xrightarrowτ 0$ for every $u\in X_+$. This convergence has been studied recently for lattice-normed vector lattices as the $up$-convergence in \cite{AGG,AEEM,AEEM2}, the $uo$-convergence in \cite{GTX}, and, as the $un$-convergence in \cite{DOT,GX,GTX,KMT,Tr2}. In this paper, we study the general properties of the unbounded $p_τ$-convergence.