Bibounded uo-convergence and b-property in vector lattices

Safak Alpay; Eduard Emelyanov; Svetlana Gorokhova

Bibounded uo-convergence and b-property in vector lattices

Functional Analysis 2020-09-17 v1

Authors: Safak Alpay , Eduard Emelyanov , Svetlana Gorokhova

Abstract

We define bidual bounded $uo$ -convergence in vector lattices and investigate relations between this convergence and $b$ -property. We prove that for a regular Riesz dual system $\langle X,X^{\sim}\rangle$ , $X$ has $b$ -property if and only if the order convergence in $X$ agrees with the order convergence in $X^{\sim\sim}$ .

Cite

@article{arxiv.2009.07401,
  title  = {Bibounded uo-convergence and b-property in vector lattices},
  author = {Safak Alpay and Eduard Emelyanov and Svetlana Gorokhova},
  journal= {arXiv preprint arXiv:2009.07401},
  year   = {2020}
}

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