Unbounded $p_\tau$-Convergence in Vector Lattices Normed by Locally Solid Lattices

Abdulla Aydın

Unbounded $p_\tau$-Convergence in Vector Lattices Normed by Locally Solid Lattices

Functional Analysis 2018-11-16 v4

Authors: Abdulla Aydın

Abstract

Let $(x_\alpha)$ be a net in a vector lattice normed by locally solid lattice $(X,p,E_\tau)$ . We say that $(x_\alpha)$ is unbounded $p_\tau$ -convergent to $x\in X$ if $p(\lvert x_\alpha-x\rvert\wedge u)\xrightarrow{\tau} 0$ 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 $p_\tau$ -convergence.

Keywords

vector lattice locally solid lattice unbounded p_tau-convergence net lattice-normed convergence properties

Cite

@article{arxiv.1711.00734,
  title  = {Unbounded $p_\tau$-Convergence in Vector Lattices Normed by Locally Solid Lattices},
  author = {Abdulla Aydın},
  journal= {arXiv preprint arXiv:1711.00734},
  year   = {2018}
}

Comments

12 pages. arXiv admin note: text overlap with arXiv:1609.05301, text overlap with arXiv:1706.02006 by other authors

Unbounded $p_\tau$-Convergence in Vector Lattices Normed by Locally Solid Lattices

Abstract

Keywords

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